Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
428 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 88 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. C8×C4⋊#6923 | C2 | semidirect |
| 2. #21461367 | C2 | semidirect |
| 3. #21461202 | C2 | semidirect |
| 5. #21461128 | C2 | semidirect |
| 24. #16840112 | C4 | semidirect |
| 25. #16840110 | C4 | semidirect |
| 26. #16840109 | C4 | semidirect |
| 30. C61×#487 | C4 | semidirect |
| 201. #487 | #6923 | semidirect |
| 219. C61 | #9751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊#6923 | 2 |
| #21461367 | 2 |
| #21461202 | 2 |
| #21461200 | 2 |
| #21461128 | 2 |
| #21461126 | 2 |
| #21456143 | 2 |
| #9751 | 61 |