Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 9. #16837781 | C4 | semidirect |
| 10. #16837752 | C4 | semidirect |
| 79. C2×C8×C59 | Q16 | semidirect |
| 182. C59 | #9290 | semidirect |
| 241. C2×C8 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435044 | 2 |
| #21433036 | 2 |
| #21422781 | 2 |
| #21422659 | 2 |
| #21421954 | 2 |
| #21421927 | 2 |
| C59×#1993 | 2 |
| #9290 | 59 |