Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#11745312 | C2 | semidirect |
| 2. #14271713 | C2 | semidirect |
| 3. #14271545 | C2 | semidirect |
| 4. #14271542 | C2 | semidirect |
| 5. #14271539 | C2 | semidirect |
| 6. #14271537 | C2 | semidirect |
| 7. #14271535 | C2 | semidirect |
| 8. C2×C4×#6597 | C2 | semidirect |
| 9. C29×#532 | C2 | semidirect |
| 57. C2×#6597 | D4 | semidirect |
| 94. C4×C29 | #135 | semidirect |
| 99. #532 | D29 | semidirect |
| 133. C29 | #3147 | semidirect |
| 196. C4 | #11745312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745312 | 2 |
| #14271713 | 2 |
| #14271545 | 2 |
| #14271542 | 2 |
| #14271539 | 2 |
| #14271537 | 2 |
| #14271535 | 2 |
| C2×C4×#6597 | 2 |
| C29×#532 | 2 |
| #3147 | 29 |