Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
362 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21435557 | C2 | semidirect |
| 2. #21426027 | C2 | semidirect |
| 4. #21425352 | C2 | semidirect |
| 5. #21422115 | C2 | semidirect |
| 6. #21422112 | C2 | semidirect |
| 7. C59×#1323 | C2 | semidirect |
| 167. #1323 | D59 | semidirect |
| 193. C59 | #12166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435557 | 2 |
| #21426027 | 2 |
| #21426010 | 2 |
| #21425352 | 2 |
| #21422115 | 2 |
| #21422112 | 2 |
| C59×#1323 | 2 |
| #12166 | 59 |