Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11745304 | C2 | semidirect |
| 3. #14271385 | C2 | semidirect |
| 4. #14271373 | C2 | semidirect |
| 5. #14271363 | C2 | semidirect |
| 6. #14271187 | C2 | semidirect |
| 7. #14271162 | C2 | semidirect |
| 8. C2×C4×Q8×C29 | C2 | semidirect |
| 36. C2×Q8×C29 | D4 | semidirect |
| 112. C4×C29 | #137 | semidirect |
| 118. C2×C4×Q8 | D29 | semidirect |
| 154. C29 | #3037 | semidirect |
| 160. C2×Q8 | D116 | semidirect |
| 233. C4 | #11745304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745304 | 2 |
| #14271713 | 2 |
| #14271385 | 2 |
| #14271373 | 2 |
| #14271363 | 2 |
| #14271187 | 2 |
| #14271162 | 2 |
| C2×C4×Q8×C29 | 2 |
| #3037 | 29 |