Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
354 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. #21426277 | C2 | semidirect |
| 3. #21426274 | C2 | semidirect |
| 4. #21425586 | C2 | semidirect |
| 5. #21422104 | C2 | semidirect |
| 6. #21422035 | C2 | semidirect |
| 7. C59×#1347 | C2 | semidirect |
| 162. #1347 | D59 | semidirect |
| 190. C59 | #12288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435402 | 2 |
| #21426277 | 2 |
| #21426274 | 2 |
| #21425586 | 2 |
| #21422104 | 2 |
| #21422035 | 2 |
| C59×#1347 | 2 |
| #12288 | 59 |