Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21426383 | C2 | semidirect |
| 3. #21423614 | C2 | semidirect |
| 4. #21422148 | C2 | semidirect |
| 5. #21422078 | C2 | semidirect |
| 68. D8×C59 | Q16 | semidirect |
| 162. C59 | #12414 | semidirect |
| 205. D8 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426383 | 2 |
| #21426243 | 2 |
| #21423614 | 2 |
| #21422148 | 2 |
| #21422078 | 2 |
| #21422063 | 2 |
| C59×#3389 | 2 |
| #12414 | 59 |