Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
280 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 280 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. #21448092 | C2 | semidirect |
| 4. #21445413 | C2 | semidirect |
| 6. #21443735 | C2 | semidirect |
| 7. C61×#2241 | C2 | semidirect |
| 68. #11758185 | SD16 | semidirect |
| 102. #2241 | D61 | semidirect |
| 126. C61 | #12508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448092 | 2 |
| #21448076 | 2 |
| #21448043 | 2 |
| #21445413 | 2 |
| #21445412 | 2 |
| #21443735 | 2 |
| C61×#2241 | 2 |
| #12508 | 61 |