Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
352 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21425893 | C2 | semidirect |
| 3. #21425850 | C2 | semidirect |
| 4. Q8⋊(C59⋊C16) | C2 | semidirect |
| 5. #21422052 | C2 | semidirect |
| 6. #21422050 | C2 | semidirect |
| 7. C59×Q8⋊C16 | C2 | semidirect |
| 105. Q8×C59 | M32 | semidirect |
| 117. D236 | M32 | semidirect |
| 157. Q8⋊C16 | D59 | semidirect |
| 184. C59 | #11623 | semidirect |
| 263. Q8 | #14273666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#11745689 | 2 |
| #21425893 | 2 |
| #21425850 | 2 |
| Q8⋊(C59⋊C16) | 2 |
| #21422052 | 2 |
| #21422050 | 2 |
| C59×Q8⋊C16 | 2 |
| #11623 | 59 |