Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
316 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21426369 | C2 | semidirect |
| 3. #21423490 | C2 | semidirect |
| 4. #21422151 | C2 | semidirect |
| 5. Q8⋊(C59⋊C16) | C2 | semidirect |
| 62. D8×C59 | Q16 | semidirect |
| 151. C59 | #12404 | semidirect |
| 190. D8 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426369 | 2 |
| #21426233 | 2 |
| #21423490 | 2 |
| #21422151 | 2 |
| Q8⋊(C59⋊C16) | 2 |
| #21422057 | 2 |
| Q8×D8×C59 | 2 |
| #12404 | 59 |