Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
240 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 240 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. #21422981 | C2 | semidirect |
| 2. D8×C59⋊C8 | C2 | semidirect |
| 3. #21422170 | C2 | semidirect |
| 4. #21422057 | C2 | semidirect |
| 5. #21422057 | C2 | semidirect |
| 6. #21422015 | C2 | semidirect |
| 51. D8×C59 | M16 | semidirect |
| 134. C59 | #12073 | semidirect |
| 163. D8 | #11745664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21422981 | 2 |
| D8×C59⋊C8 | 2 |
| #21422170 | 2 |
| #21422057 | 2 |
| #21422015 | 2 |
| C4×D16×C59 | 2 |
| #12073 | 59 |