Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13094017 | C2 | semidirect |
| 2. #13094017 | C2 | semidirect |
| 3. #13094010 | C2 | semidirect |
| 4. #13094008 | C2 | semidirect |
| 5. #13094007 | C2 | semidirect |
| 6. #13094006 | C2 | semidirect |
| 7. #13094003 | C2 | semidirect |
| 8. #13094001 | C2 | semidirect |
| 10. C4×C22⋊D47 | C2 | semidirect |
| 11. (C22⋊D47)⋊C4 | C2 | semidirect |
| 12. #13093983 | C2 | semidirect |
| 13. #13093980 | C2 | semidirect |
| 14. C2×C22⋊Dic47 | C2 | semidirect |
| 15. C2×C22⋊C4×C47 | C2 | semidirect |
| 24. C2×C4×D47 | C22 | semidirect |
| 25. C2×Dic94 | C22 | semidirect |
| 37. (C2×D47)⋊C4 | C22 | semidirect |
| 38. (C2×D47)⋊C4 | C22 | semidirect |
| 39. (C2×D47)⋊C4 | C22 | semidirect |
| 40. C4⋊Dic47 | C22 | semidirect |
| 41. C4⋊Dic47 | C22 | semidirect |
| 42. C4⋊Dic47 | C22 | semidirect |
| 43. Dic47⋊C4 | C22 | semidirect |
| 44. Dic47⋊C4 | C22 | semidirect |
| 45. Dic47⋊C4 | C22 | semidirect |
| 46. Dic47⋊C4 | C22 | semidirect |
| 47. Dic47⋊C4 | C22 | semidirect |
| 48. C4×Dic47 | C22 | semidirect |
| 49. C4×Dic47 | C22 | semidirect |
| 50. C4×Dic47 | C22 | semidirect |
| 111. C47 | #551 | semidirect |
| 126. C2×C22⋊C4 | D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13094017 | 2 |
| #13094010 | 2 |
| #13094008 | 2 |
| #13094007 | 2 |
| #13094006 | 2 |
| #13094003 | 2 |
| #13094001 | 2 |
| #13093993 | 2 |
| C4×C22⋊D47 | 2 |
| (C22⋊D47)⋊C4 | 2 |
| #13093983 | 2 |
| #13093980 | 2 |
| C2×C22⋊Dic47 | 2 |
| C2×C22⋊C4×C47 | 2 |
| #551 | 47 |