Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14557936 | C2 | semidirect |
| 3. #14557912 | C2 | semidirect |
| 4. #14557885 | C2 | semidirect |
| 5. #14557883 | C2 | semidirect |
| 7. C4×#10596942 | C2 | semidirect |
| 73. C2×C4×C37 | Q16 | semidirect |
| 114. C37 | #3170 | semidirect |
| 182. C2×C4 | #10596942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558090 | 2 |
| #14557936 | 2 |
| #14557912 | 2 |
| #14557885 | 2 |
| #14557883 | 2 |
| #14557772 | 2 |
| C4×#10596942 | 2 |
| C2×C4×#64436 | 2 |
| C37×#533 | 2 |
| #3170 | 37 |