Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
166 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 66 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. #14558397 | C2 | semidirect |
| 4. #14558396 | C2 | semidirect |
| 5. #14558395 | C2 | semidirect |
| 6. #14558394 | C2 | semidirect |
| 58. C8×C37 | M16 | semidirect |
| 60. #64436 | M16 | semidirect |
| 85. C37 | #1569 | semidirect |
| 138. C8 | #10596957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558554 | 2 |
| #14558536 | 2 |
| #14558397 | 2 |
| #14558396 | 2 |
| #14558395 | 2 |
| #14558394 | 2 |
| M16×Dic37 | 2 |
| #1569 | 37 |