Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
622 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21435079 | C2 | semidirect |
| 2. #21435011 | C2 | semidirect |
| 3. C2×#16837791 | C2 | semidirect |
| 4. #21422809 | C2 | semidirect |
| 5. #21422449 | C2 | semidirect |
| 6. #21421995 | C2 | semidirect |
| 7. C59×#1530 | C2 | semidirect |
| 199. #1530 | D59 | semidirect |
| 232. C59 | #10128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435079 | 2 |
| #21435011 | 2 |
| C2×#16837791 | 2 |
| #21422809 | 2 |
| #21422449 | 2 |
| #21421995 | 2 |
| C59×#1530 | 2 |
| #10128 | 59 |