Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 1. C2×#11745280 | C2 | semidirect |
| 3. C4⋊Q8×D29 | C2 | semidirect |
| 4. #14271556 | C2 | semidirect |
| 5. #14271542 | C2 | semidirect |
| 6. #14271537 | C2 | semidirect |
| 7. #14271536 | C2 | semidirect |
| 8. C4×#90772 | C2 | semidirect |
| 9. C29×#494 | C2 | semidirect |
| 59. #90772 | D4 | semidirect |
| 90. C4×C29 | #137 | semidirect |
| 100. #494 | D29 | semidirect |
| 130. C29 | #3152 | semidirect |
| 191. C4 | #11745280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745280 | 2 |
| #14271714 | 2 |
| C4⋊Q8×D29 | 2 |
| #14271556 | 2 |
| #14271542 | 2 |
| #14271537 | 2 |
| #14271536 | 2 |
| C4×#90772 | 2 |
| C29×#494 | 2 |
| #3152 | 29 |