Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21447631 | C2 | semidirect |
| 3. #21443796 | C2 | semidirect |
| 4. #21443793 | C2 | semidirect |
| 5. C61×#1455 | C2 | semidirect |
| 14. #16839583 | C22 | semidirect |
| 20. C61×#322 | C22 | semidirect |
| 21. C82×C61 | C22 | semidirect |
| 74. Dic244 | M16 | semidirect |
| 76. D488 | M16 | semidirect |
| 123. #1455 | D61 | semidirect |
| 144. #322 | C2×D61 | semidirect |
| 145. C82 | C2×D61 | semidirect |
| 146. C61 | #11669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454730 | 2 |
| #21447631 | 2 |
| #21443796 | 2 |
| #21443793 | 2 |
| C61×#1455 | 2 |
| #11669 | 61 |