Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1140 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 175 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. #21432378 | C2 | semidirect |
| 2. #21425522 | C2 | semidirect |
| 3. #21425278 | C2 | semidirect |
| 4. #21425275 | C2 | semidirect |
| 5. #21425092 | C2 | semidirect |
| 6. #21424006 | C2 | semidirect |
| 7. C59×#2847 | C2 | semidirect |
| 8. C22×#11745669 | C22 | semidirect |
| 11. C2×#14273660 | C22 | semidirect |
| 12. C2×#14273648 | C22 | semidirect |
| 13. C2×#14273647 | C22 | semidirect |
| 18. #16837164 | C22 | semidirect |
| 19. #16837164 | C22 | semidirect |
| 59. C24×C59 | D8 | semidirect |
| 165. #2847 | D59 | semidirect |
| 194. C59 | #32706 | semidirect |
| 230. C24 | #11745669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432378 | 2 |
| #21425522 | 2 |
| #21425278 | 2 |
| #21425275 | 2 |
| #21425092 | 2 |
| #21424006 | 2 |
| C59×#2847 | 2 |
| #32706 | 59 |