Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21448044 | C2 | semidirect |
| 3. #21445179 | C2 | semidirect |
| 4. #21443874 | C2 | semidirect |
| 5. Q8⋊#11758185 | C2 | semidirect |
| 6. #21443780 | C2 | semidirect |
| 7. Q8×D8×C61 | C2 | semidirect |
| 65. D8×C61 | SD16 | semidirect |
| 92. Q8×C61 | D16 | semidirect |
| 132. Q8×D8 | D61 | semidirect |
| 161. C61 | #12352 | semidirect |
| 206. D8 | #11758201 | semidirect |
| 229. Q8 | #14519718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448044 | 2 |
| #21447854 | 2 |
| #21445179 | 2 |
| #21443874 | 2 |
| Q8⋊#11758185 | 2 |
| #21443780 | 2 |
| Q8×D8×C61 | 2 |
| #12352 | 61 |