Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1082 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 163 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. #21438501 | C2 | semidirect |
| 2. #21435474 | C2 | semidirect |
| 3. #21423239 | C2 | semidirect |
| 4. #21423210 | C2 | semidirect |
| 5. #21423177 | C2 | semidirect |
| 6. #21423148 | C2 | semidirect |
| 7. #21422831 | C2 | semidirect |
| 8. #21422548 | C2 | semidirect |
| 9. C59×#3147 | C2 | semidirect |
| 19. #16837689 | C22 | semidirect |
| 22. #16837594 | C22 | semidirect |
| 23. #16837426 | C22 | semidirect |
| 24. #16837151 | C22 | semidirect |
| 26. #16837131 | C22 | semidirect |
| 27. #16837131 | C22 | semidirect |
| 30. C59×#532 | C22 | semidirect |
| 32. C59×#494 | C22 | semidirect |
| 35. C59×#492 | C22 | semidirect |
| 36. C2×C4×C8×C59 | C22 | semidirect |
| 202. #3147 | D59 | semidirect |
| 225. #532 | C2×D59 | semidirect |
| 227. #494 | C2×D59 | semidirect |
| 230. #492 | C2×D59 | semidirect |
| 237. C2×C4×C8 | C2×D59 | semidirect |
| 242. C59 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438501 | 2 |
| #21435474 | 2 |
| #21423239 | 2 |
| #21423210 | 2 |
| #21423177 | 2 |
| #21423148 | 2 |
| #21422831 | 2 |
| #21422548 | 2 |
| C59×#3147 | 2 |
| #18686 | 59 |