Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1380 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 195 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. C23×D472 | C2 | semidirect |
| 2. C2×#16837840 | C2 | semidirect |
| 3. #21433677 | C2 | semidirect |
| 4. #21426027 | C2 | semidirect |
| 5. #21426010 | C2 | semidirect |
| 6. #21425813 | C2 | semidirect |
| 7. C59×#2112 | C2 | semidirect |
| 9. C2×#14273749 | C22 | semidirect |
| 17. C2×#14273672 | C22 | semidirect |
| 18. C2×D944 | C22 | semidirect |
| 19. #16837643 | C22 | semidirect |
| 20. #16837638 | C22 | semidirect |
| 22. #16837440 | C22 | semidirect |
| 24. #16837204 | C22 | semidirect |
| 26. C2×M32×C59 | C22 | semidirect |
| 27. C59×C22⋊C16 | C22 | semidirect |
| 37. C2×Dic236 | C23 | semidirect |
| 45. C2×D472 | D4 | semidirect |
| 47. C2×D472 | C23 | semidirect |
| 56. #14273661 | C23 | semidirect |
| 67. C2×C16×C59 | C23 | semidirect |
| 159. C22×C59 | #509 | semidirect |
| 179. #2112 | D59 | semidirect |
| 198. C2×M32 | C2×D59 | semidirect |
| 205. C22⋊C16 | C2×D59 | semidirect |
| 206. C59 | #33517 | semidirect |
| 242. C2×C16 | C22×D59 | semidirect |
| 343. C22 | #16837840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D472 | 2 |
| C2×#16837840 | 2 |
| #21433677 | 2 |
| #21426027 | 2 |
| #21426010 | 2 |
| #21425813 | 2 |
| C59×#2112 | 2 |
| #33517 | 59 |