Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 166 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×#11745348 | C2 | semidirect |
| 2. #14272197 | C2 | semidirect |
| 3. #14272193 | C2 | semidirect |
| 4. #14272191 | C2 | semidirect |
| 5. D29⋊(C4⋊C8) | C2 | semidirect |
| 6. #14272138 | C2 | semidirect |
| 7. C4×#90796 | C2 | semidirect |
| 48. #90796 | D4 | semidirect |
| 94. C4×C29 | #131 | semidirect |
| 134. C29 | #2935 | semidirect |
| 201. C4 | #11745348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745348 | 2 |
| #14272197 | 2 |
| #14272193 | 2 |
| #14272191 | 2 |
| D29⋊(C4⋊C8) | 2 |
| #14272138 | 2 |
| C4×#90796 | 2 |
| #14271714 | 2 |
| #2935 | 29 |