Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
398 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 4. #21421989 | C2 | semidirect |
| 5. #21421960 | C2 | semidirect |
| 6. #21421952 | C2 | semidirect |
| 7. C59×#2605 | C2 | semidirect |
| 29. #14273727 | Q8 | semidirect |
| 30. #14273724 | Q8 | semidirect |
| 176. #2605 | D59 | semidirect |
| 208. C59 | #10378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425014 | 2 |
| #21422642 | 2 |
| #21422603 | 2 |
| #21421989 | 2 |
| #21421960 | 2 |
| #21421952 | 2 |
| C59×#2605 | 2 |
| #10378 | 59 |