Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
222 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 222 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 |
|---|---|---|
| 1. Q8×C59⋊C16 | C2 | semidirect |
| 3. #21422166 | C2 | semidirect |
| 4. Q8⋊(C59⋊C16) | C2 | semidirect |
| 6. #21422014 | C2 | semidirect |
| 70. Q8×C59 | M32 | semidirect |
| 128. C59 | #12056 | semidirect |
| 176. Q8 | #14273667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C59⋊C16 | 2 |
| #21425928 | 2 |
| #21422166 | 2 |
| Q8⋊(C59⋊C16) | 2 |
| D4⋊(C59⋊C16) | 2 |
| #21422014 | 2 |
| C8×SD16×C59 | 2 |
| #12056 | 59 |