Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
646 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 646 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. #21437238 | C2 | semidirect |
| 2. #21435881 | C2 | semidirect |
| 3. #21426223 | C2 | semidirect |
| 4. #21426162 | C2 | semidirect |
| 5. #21426073 | C2 | semidirect |
| 6. #21426052 | C2 | semidirect |
| 7. #21425978 | C2 | semidirect |
| 8. #21425934 | C2 | semidirect |
| 9. C59×#2249 | C2 | semidirect |
| 12. #16838203 | C22 | semidirect |
| 13. #16837843 | C22 | semidirect |
| 20. #16837818 | C22 | semidirect |
| 21. #16837674 | C22 | semidirect |
| 27. #16837520 | C22 | semidirect |
| 28. #16837232 | C22 | semidirect |
| 29. #16837223 | C22 | semidirect |
| 30. #16837218 | C22 | semidirect |
| 31. #16837215 | C22 | semidirect |
| 32. #16837210 | C22 | semidirect |
| 33. #16837185 | C22 | semidirect |
| 34. C2×Q32×C59 | C22 | semidirect |
| 35. C2×SD32×C59 | C22 | semidirect |
| 37. C59×#495 | C22 | semidirect |
| 38. C4×C16×C59 | C22 | semidirect |
| 179. #2249 | D59 | semidirect |
| 200. C2×Q32 | C2×D59 | semidirect |
| 202. C2×SD32 | C2×D59 | semidirect |
| 205. #495 | C2×D59 | semidirect |
| 219. C4×C16 | C2×D59 | semidirect |
| 220. C59 | #33857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437238 | 2 |
| #21435881 | 2 |
| #21426223 | 2 |
| #21426162 | 2 |
| #21426073 | 2 |
| #21426052 | 2 |
| #21425978 | 2 |
| #21425934 | 2 |
| C59×#2249 | 2 |
| #33857 | 59 |