Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
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×C29 | C2 | semidirect |
| 3. C2×C22⋊Dic29 | C2 | semidirect |
| 4. #11745291 | C2 | semidirect |
| 5. C4×C22⋊D29 | C2 | semidirect |
| 6. #11745288 | C2 | semidirect |
| 7. #11745286 | C2 | semidirect |
| 8. #11745248 | C2 | semidirect |
| 9. #11745247 | C2 | semidirect |
| 10. #11745245 | C2 | semidirect |
| 11. #11745243 | C2 | semidirect |
| 12. #11745241 | C2 | semidirect |
| 13. #11745241 | C2 | semidirect |
| 14. #11745240 | C2 | semidirect |
| 15. #11745239 | C2 | semidirect |
| 24. C2×C4×D29 | C22 | semidirect |
| 25. C2×Dic58 | C22 | semidirect |
| 37. #90781 | C22 | semidirect |
| 38. #90781 | C22 | semidirect |
| 39. #90781 | C22 | semidirect |
| 40. C4⋊Dic29 | C22 | semidirect |
| 41. C4⋊Dic29 | C22 | semidirect |
| 42. C4⋊Dic29 | C22 | semidirect |
| 43. #90779 | C22 | semidirect |
| 44. #90779 | C22 | semidirect |
| 45. #90779 | C22 | semidirect |
| 46. #90779 | C22 | semidirect |
| 47. #90779 | C22 | semidirect |
| 48. C4×Dic29 | C22 | semidirect |
| 49. C4×Dic29 | C22 | semidirect |
| 50. C4×Dic29 | C22 | semidirect |
| 125. C2×C22⋊C4 | D29 | semidirect |
| 126. C29 | #551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊C4×C29 | 2 |
| #11745315 | 2 |
| C2×C22⋊Dic29 | 2 |
| #11745291 | 2 |
| C4×C22⋊D29 | 2 |
| #11745288 | 2 |
| #11745286 | 2 |
| #11745248 | 2 |
| #11745247 | 2 |
| #11745245 | 2 |
| #11745243 | 2 |
| #11745241 | 2 |
| #11745240 | 2 |
| #11745239 | 2 |
| #551 | 29 |