Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
454 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21427390 | C2 | semidirect |
| 5. #21421997 | C2 | semidirect |
| 6. #21421924 | C2 | semidirect |
| 7. C59×#1303 | C2 | semidirect |
| 29. #14273727 | Q8 | semidirect |
| 30. #14273724 | Q8 | semidirect |
| 195. #1303 | D59 | semidirect |
| 222. C59 | #10370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427390 | 2 |
| #21424927 | 2 |
| #21422592 | 2 |
| #21422590 | 2 |
| #21421997 | 2 |
| #21421924 | 2 |
| C59×#1303 | 2 |
| #10370 | 59 |