Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
536 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21434746 | C2 | semidirect |
| 2. #21433000 | C2 | semidirect |
| 3. #21426311 | C2 | semidirect |
| 4. #21426273 | C2 | semidirect |
| 5. #21426173 | C2 | semidirect |
| 6. #21426044 | C2 | semidirect |
| 7. #21425996 | C2 | semidirect |
| 8. C59×#2166 | C2 | semidirect |
| 13. #16837804 | C22 | semidirect |
| 14. #16837779 | C22 | semidirect |
| 22. #16837515 | C22 | semidirect |
| 26. #16837225 | C22 | semidirect |
| 27. #16837216 | C22 | semidirect |
| 30. C59×#364 | C22 | semidirect |
| 32. C59×#347 | C22 | semidirect |
| 169. #2166 | D59 | semidirect |
| 194. #364 | C2×D59 | semidirect |
| 198. #347 | C2×D59 | semidirect |
| 199. C59 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434746 | 2 |
| #21433000 | 2 |
| #21426311 | 2 |
| #21426273 | 2 |
| #21426173 | 2 |
| #21426044 | 2 |
| #21425996 | 2 |
| C59×#2166 | 2 |
| #33692 | 59 |