Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #21422076 | C2 | semidirect |
| 5. Q8⋊(C59⋊C16) | C2 | semidirect |
| 6. #21422074 | C2 | semidirect |
| 7. C59×Q8⋊C16 | C2 | semidirect |
| 148. Q8⋊C16 | D59 | semidirect |
| 172. C59 | #11640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433025 | 2 |
| #21425898 | 2 |
| #21425893 | 2 |
| #21422076 | 2 |
| Q8⋊(C59⋊C16) | 2 |
| #21422074 | 2 |
| C59×Q8⋊C16 | 2 |
| #11640 | 59 |