Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1262 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1262 conjugacy classes of subgroups — too many to draw. Only its 191 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. #21459590 | C2 | semidirect |
| 2. #21456737 | C2 | semidirect |
| 3. #21444753 | C2 | semidirect |
| 4. #21444313 | C2 | semidirect |
| 5. #21444143 | C2 | semidirect |
| 6. C61×#2548 | C2 | semidirect |
| 78. C2×Q8×C61 | D8 | semidirect |
| 192. #2548 | D61 | semidirect |
| 225. C61 | #18401 | semidirect |
| 283. C2×Q8 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21459590 | 2 |
| #21456737 | 2 |
| #21444753 | 2 |
| #21444313 | 2 |
| #21444143 | 2 |
| C61×#2548 | 2 |
| #18401 | 61 |