Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
222 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #21422165 | C2 | semidirect |
| 4. Q8⋊(C59⋊C16) | C2 | semidirect |
| 6. #21422015 | C2 | semidirect |
| 7. Q8×C16×C59 | C2 | semidirect |
| 70. Q8×C59 | M32 | semidirect |
| 102. Q8×C16 | D59 | semidirect |
| 128. C59 | #12056 | semidirect |
| 176. Q8 | #14273666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425929 | 2 |
| C8×#11745671 | 2 |
| #21422165 | 2 |
| Q8⋊(C59⋊C16) | 2 |
| #21422050 | 2 |
| #21422015 | 2 |
| Q8×C16×C59 | 2 |
| #12056 | 59 |