Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 364 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. #21425898 | C2 | semidirect |
| 3. #21425893 | C2 | semidirect |
| 4. #21422052 | C2 | semidirect |
| 5. D4⋊(C59⋊C16) | C2 | semidirect |
| 6. #21422050 | C2 | semidirect |
| 7. C59×D4⋊C16 | C2 | semidirect |
| 170. D4⋊C16 | D59 | semidirect |
| 196. C59 | #11632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432803 | 2 |
| #21425898 | 2 |
| #21425893 | 2 |
| #21422052 | 2 |
| D4⋊(C59⋊C16) | 2 |
| #21422050 | 2 |
| C59×D4⋊C16 | 2 |
| #11632 | 59 |