Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14558261 | C2 | semidirect |
| 3. #14557883 | C2 | semidirect |
| 4. #14557840 | C2 | semidirect |
| 7. #14557740 | C2 | semidirect |
| 8. Q8×#64436 | C2 | semidirect |
| 9. C4×#10596942 | C2 | semidirect |
| 127. C37 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558261 | 2 |
| #14557887 | 2 |
| #14557883 | 2 |
| #14557840 | 2 |
| #14557813 | 2 |
| #14557752 | 2 |
| #14557740 | 2 |
| Q8×#64436 | 2 |
| C4×#10596942 | 2 |
| C4×#10596940 | 2 |
| C37×#556 | 2 |
| #3364 | 37 |