Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
304 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 73 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. Q8×Dic236 | C2 | semidirect |
| 5. #21422153 | C2 | semidirect |
| 6. #21422061 | C2 | semidirect |
| 7. C59×Q8⋊C16 | C2 | semidirect |
| 78. Dic236 | SD16 | semidirect |
| 86. Q8×C59 | SD32 | semidirect |
| 129. Q8⋊C16 | D59 | semidirect |
| 152. C59 | #12354 | semidirect |
| 218. Q8 | #14273672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic236 | 2 |
| #21426320 | 2 |
| #21426137 | 2 |
| #21423456 | 2 |
| #21422153 | 2 |
| #21422061 | 2 |
| C59×Q8⋊C16 | 2 |
| #12354 | 59 |