Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
306 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21425700 | C2 | semidirect |
| 4. #21424874 | C2 | semidirect |
| 5. #21422211 | C2 | semidirect |
| 6. #21422203 | C2 | semidirect |
| 15. #16837218 | C4 | semidirect |
| 16. #16837215 | C4 | semidirect |
| 162. C59 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425845 | 2 |
| #21425700 | 2 |
| #21424995 | 2 |
| #21424874 | 2 |
| #21422211 | 2 |
| #21422203 | 2 |
| C2×C59×#360 | 2 |
| #13156 | 59 |