Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #21433186 | C2 | semidirect |
| 3. #21422544 | C2 | semidirect |
| 5. #21421965 | C2 | semidirect |
| 6. #21421947 | C2 | semidirect |
| 242. C59 | #9244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837621 | 2 |
| #21433186 | 2 |
| #21422544 | 2 |
| #21422448 | 2 |
| #21421965 | 2 |
| #21421947 | 2 |
| C59×#1527 | 2 |
| #9244 | 59 |