Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
378 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21434635 | C2 | semidirect |
| 4. #21422206 | C2 | semidirect |
| 5. #21422193 | C2 | semidirect |
| 6. #21422185 | C2 | semidirect |
| 51. C2×D8×C59 | Q8 | semidirect |
| 183. C59 | #13369 | semidirect |
| 190. C2×D8 | Dic118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434635 | 2 |
| #21425812 | 2 |
| C2×#16837203 | 2 |
| #21422206 | 2 |
| #21422193 | 2 |
| #21422185 | 2 |
| C59×#1978 | 2 |
| #13369 | 59 |