Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 151 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. #21437237 | C2 | semidirect |
| 2. #21435896 | C2 | semidirect |
| 3. #21426346 | C2 | semidirect |
| 4. #21426216 | C2 | semidirect |
| 5. #21426173 | C2 | semidirect |
| 6. #21426055 | C2 | semidirect |
| 7. #21425978 | C2 | semidirect |
| 8. C59×#2170 | C2 | semidirect |
| 9. #16838207 | C22 | semidirect |
| 12. #16837840 | C22 | semidirect |
| 16. C2×D944 | C22 | semidirect |
| 17. C2×D944 | C22 | semidirect |
| 18. #16837779 | C22 | semidirect |
| 20. #16837672 | C22 | semidirect |
| 22. #16837520 | C22 | semidirect |
| 23. #16837232 | C22 | semidirect |
| 24. #16837216 | C22 | semidirect |
| 25. #16837210 | C22 | semidirect |
| 26. C59×#504 | C22 | semidirect |
| 28. C59×#364 | C22 | semidirect |
| 29. C59×#350 | C22 | semidirect |
| 30. C4×C16×C59 | C22 | semidirect |
| 45. Dic472 | D4 | semidirect |
| 47. #14273672 | D4 | semidirect |
| 52. D944 | D4 | semidirect |
| 145. #2170 | D59 | semidirect |
| 160. #504 | C2×D59 | semidirect |
| 168. #364 | C2×D59 | semidirect |
| 171. #350 | 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 |
|---|---|
| #21437237 | 2 |
| #21435896 | 2 |
| #21426346 | 2 |
| #21426216 | 2 |
| #21426173 | 2 |
| #21426055 | 2 |
| #21425978 | 2 |
| C59×#2170 | 2 |
| #33858 | 59 |