Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 12. C59×#500 | C4 | semidirect |
| 13. C59×#494 | C4 | semidirect |
| 18. C4×Q16×C59 | C4 | semidirect |
| 123. #500 | Dic59 | semidirect |
| 124. #494 | Dic59 | semidirect |
| 129. C4×Q16 | Dic59 | semidirect |
| 137. C59 | #11745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425899 | 2 |
| C4×#14273659 | 2 |
| #21422108 | 2 |
| C59×#3170 | 2 |
| #11745 | 59 |