Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
922 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21425035 | C2 | semidirect |
| 3. #21422789 | C2 | semidirect |
| 4. #21422708 | C2 | semidirect |
| 5. #21422707 | C2 | semidirect |
| 6. #21422439 | C2 | semidirect |
| 7. C59×#1551 | C2 | semidirect |
| 222. #1551 | D59 | semidirect |
| 257. C59 | #8459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437862 | 2 |
| #21425035 | 2 |
| #21422789 | 2 |
| #21422708 | 2 |
| #21422707 | 2 |
| #21422439 | 2 |
| C59×#1551 | 2 |
| #8459 | 59 |