Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
404 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 404 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. #21426046 | C2 | semidirect |
| 2. #21426041 | C2 | semidirect |
| 3. #21425200 | C2 | semidirect |
| 4. #21422090 | C2 | semidirect |
| 5. #21422087 | C2 | semidirect |
| 6. #21422034 | C2 | semidirect |
| 7. C59×#3204 | C2 | semidirect |
| 185. #3204 | D59 | semidirect |
| 217. C59 | #12119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426046 | 2 |
| #21426041 | 2 |
| #21425200 | 2 |
| #21422090 | 2 |
| #21422087 | 2 |
| #21422034 | 2 |
| C59×#3204 | 2 |
| #12119 | 59 |