Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #21444504 | C2 | semidirect |
| 5. #21443677 | C2 | semidirect |
| 6. #21443650 | C2 | semidirect |
| 7. C61×#1993 | C2 | semidirect |
| 10. #16840136 | C4 | semidirect |
| 11. #16840112 | C4 | semidirect |
| 89. C2×C8×C61 | SD16 | semidirect |
| 171. #1993 | D61 | semidirect |
| 201. C61 | #9289 | semidirect |
| 272. C2×C8 | #11758201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456744 | 2 |
| #21454538 | 2 |
| #21444504 | 2 |
| #21444378 | 2 |
| #21443677 | 2 |
| #21443650 | 2 |
| C61×#1993 | 2 |
| #9289 | 61 |