Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
602 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21456396 | C2 | semidirect |
| 2. #21448094 | C2 | semidirect |
| 3. #21448042 | C2 | semidirect |
| 4. #21447902 | C2 | semidirect |
| 5. D16×Dic61 | C2 | semidirect |
| 6. C4×C16×D61 | C2 | semidirect |
| 7. C61×#2246 | C2 | semidirect |
| 75. C16×C61 | #41 | semidirect |
| 95. C4×D61 | D16 | semidirect |
| 119. #2246 | D61 | semidirect |
| 145. C61 | #33733 | semidirect |
| 198. C16 | #11758224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456396 | 2 |
| #21448094 | 2 |
| #21448042 | 2 |
| #21447902 | 2 |
| D16×Dic61 | 2 |
| C4×C16×D61 | 2 |
| C61×#2246 | 2 |
| #33733 | 61 |