Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21447412 | C2 | semidirect |
| 3. #334×D61 | C2 | semidirect |
| 4. #21443789 | C2 | semidirect |
| 5. #21443787 | C2 | semidirect |
| 6. #21443785 | C2 | semidirect |
| 7. C61×#1334 | C2 | semidirect |
| 29. #14519800 | C8 | semidirect |
| 75. Q16×C61 | C2×C8 | semidirect |
| 98. D488 | C2×C8 | semidirect |
| 157. #1334 | D61 | semidirect |
| 184. C61 | #11598 | semidirect |
| 233. Q16 | C8×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519800 | 2 |
| #21447412 | 2 |
| #334×D61 | 2 |
| #21443789 | 2 |
| #21443787 | 2 |
| #21443785 | 2 |
| C61×#1334 | 2 |
| #11598 | 61 |