Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #21422294 | C2 | semidirect |
| 4. #21422289 | C2 | semidirect |
| 5. C59×#2247 | C2 | semidirect |
| 76. #2247 | D59 | semidirect |
| 94. C59 | #13693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426414 | 2 |
| #21425978 | 2 |
| #21422294 | 2 |
| #21422289 | 2 |
| C59×#2247 | 2 |
| #13693 | 59 |