Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
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. C2×C22⋊C4×C23 | C2 | semidirect |
| 3. C2×C22⋊Dic23 | C2 | semidirect |
| 4. #10625100 | C2 | semidirect |
| 5. C4×C22⋊D23 | C2 | semidirect |
| 6. #10625097 | C2 | semidirect |
| 7. #10625095 | C2 | semidirect |
| 8. #10625057 | C2 | semidirect |
| 9. #10625056 | C2 | semidirect |
| 10. #10625054 | C2 | semidirect |
| 11. (C22⋊D23)⋊C4 | C2 | semidirect |
| 12. #10625050 | C2 | semidirect |
| 13. #10625050 | C2 | semidirect |
| 14. #10625049 | C2 | semidirect |
| 15. #10625048 | C2 | semidirect |
| 24. C2×C4×D23 | C22 | semidirect |
| 25. C2×Dic46 | C22 | semidirect |
| 37. (C2×D23)⋊C4 | C22 | semidirect |
| 38. (C2×D23)⋊C4 | C22 | semidirect |
| 39. (C2×D23)⋊C4 | C22 | semidirect |
| 40. C4⋊Dic23 | C22 | semidirect |
| 41. C4⋊Dic23 | C22 | semidirect |
| 42. C4⋊Dic23 | C22 | semidirect |
| 43. Dic23⋊C4 | C22 | semidirect |
| 44. Dic23⋊C4 | C22 | semidirect |
| 45. Dic23⋊C4 | C22 | semidirect |
| 46. Dic23⋊C4 | C22 | semidirect |
| 47. Dic23⋊C4 | C22 | semidirect |
| 48. C4×Dic23 | C22 | semidirect |
| 49. C4×Dic23 | C22 | semidirect |
| 50. C4×Dic23 | C22 | semidirect |
| 125. C2×C22⋊C4 | D23 | semidirect |
| 126. C23 | #551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊C4×C23 | 2 |
| #10625124 | 2 |
| C2×C22⋊Dic23 | 2 |
| #10625100 | 2 |
| C4×C22⋊D23 | 2 |
| #10625097 | 2 |
| #10625095 | 2 |
| #10625057 | 2 |
| #10625056 | 2 |
| #10625054 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| #10625050 | 2 |
| #10625049 | 2 |
| #10625048 | 2 |
| #551 | 23 |