Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 488 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. #21436500 | C2 | semidirect |
| 2. #21426375 | C2 | semidirect |
| 3. #21426285 | C2 | semidirect |
| 4. #21426275 | C2 | semidirect |
| 5. #21426253 | C2 | semidirect |
| 6. #21426196 | C2 | semidirect |
| 7. #21425929 | C2 | semidirect |
| 8. #21425881 | C2 | semidirect |
| 9. C4×D16×C59 | C2 | semidirect |
| 140. C4×D16 | D59 | semidirect |
| 173. C59 | #33922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436500 | 2 |
| #21426375 | 2 |
| #21426285 | 2 |
| #21426275 | 2 |
| #21426253 | 2 |
| #21426196 | 2 |
| #21425929 | 2 |
| #21425881 | 2 |
| C4×D16×C59 | 2 |
| #33922 | 59 |