Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11924555 | C2 | semidirect |
| 2. #14558187 | C2 | semidirect |
| 3. #14557913 | C2 | semidirect |
| 4. #14557775 | C2 | semidirect |
| 5. #14557738 | C2 | semidirect |
| 6. #14557696 | C2 | semidirect |
| 7. C8×D148 | C2 | semidirect |
| 8. C4×D8×C37 | C2 | semidirect |
| 38. D8×C37 | D4 | semidirect |
| 85. C4×C37 | #135 | semidirect |
| 102. C4×D8 | D37 | semidirect |
| 104. C37 | #3283 | semidirect |
| 137. D8 | D148 | semidirect |
| 183. C4 | #11924555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924555 | 2 |
| #14558187 | 2 |
| #14557913 | 2 |
| #14557775 | 2 |
| #14557738 | 2 |
| #14557696 | 2 |
| C8×D148 | 2 |
| C4×D8×C37 | 2 |
| #3283 | 37 |