Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
468 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21426371 | C2 | semidirect |
| 3. #21426303 | C2 | semidirect |
| 4. #21426238 | C2 | semidirect |
| 5. #21426184 | C2 | semidirect |
| 7. #21425877 | C2 | semidirect |
| 8. C4×Q32×C59 | C2 | semidirect |
| 114. C4×Q32 | D59 | semidirect |
| 140. C59 | #33909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436528 | 2 |
| #21426371 | 2 |
| #21426303 | 2 |
| #21426238 | 2 |
| #21426184 | 2 |
| C16×D236 | 2 |
| #21425877 | 2 |
| C4×Q32×C59 | 2 |
| #33909 | 59 |