Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
668 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21437233 | C2 | semidirect |
| 2. #21435895 | C2 | semidirect |
| 3. #21426213 | C2 | semidirect |
| 4. #21426169 | C2 | semidirect |
| 5. #21426052 | C2 | semidirect |
| 6. #21425978 | C2 | semidirect |
| 7. #21425934 | C2 | semidirect |
| 8. C59×#2246 | C2 | semidirect |
| 10. #16838203 | C22 | semidirect |
| 11. #16837838 | C22 | semidirect |
| 16. #16837818 | C22 | semidirect |
| 18. #16837669 | C22 | semidirect |
| 21. #16837520 | C22 | semidirect |
| 22. #16837232 | C22 | semidirect |
| 23. #16837223 | C22 | semidirect |
| 24. #16837215 | C22 | semidirect |
| 25. #16837210 | C22 | semidirect |
| 26. #16837185 | C22 | semidirect |
| 27. C2×D16×C59 | C22 | semidirect |
| 28. C2×D16×C59 | C22 | semidirect |
| 29. C59×#493 | C22 | semidirect |
| 30. C4×C16×C59 | C22 | semidirect |
| 44. Dic472 | D4 | semidirect |
| 45. #14273672 | D4 | semidirect |
| 47. D944 | D4 | semidirect |
| 140. #2246 | D59 | semidirect |
| 158. C2×D16 | C2×D59 | semidirect |
| 159. C2×D16 | C2×D59 | semidirect |
| 161. #493 | C2×D59 | semidirect |
| 172. C4×C16 | C2×D59 | semidirect |
| 173. C59 | #33858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437233 | 2 |
| #21435895 | 2 |
| #21426213 | 2 |
| #21426169 | 2 |
| #21426052 | 2 |
| #21425978 | 2 |
| #21425934 | 2 |
| C59×#2246 | 2 |
| #33858 | 59 |