Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 454 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. #16837754 | C4 | semidirect |
| 91. C42×C59 | Q16 | semidirect |
| 192. C59 | #9297 | semidirect |
| 268. C42 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435041 | 2 |
| #21426844 | 2 |
| #21422778 | 2 |
| #21422660 | 2 |
| #21421956 | 2 |
| #21421925 | 2 |
| C59×#1995 | 2 |
| #9297 | 59 |