Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #14271646 | C2 | semidirect |
| 3. #14271169 | C2 | semidirect |
| 4. #14271065 | C2 | semidirect |
| 5. #14270931 | C2 | semidirect |
| 6. #14270923 | C2 | semidirect |
| 7. C2×C29×#104 | C2 | semidirect |
| 13. #11745311 | C4 | semidirect |
| 46. C2×D116 | C2×C4 | semidirect |
| 65. #90777 | C2×C4 | semidirect |
| 75. Q8×C29 | C22⋊C4 | semidirect |
| 79. D4×C29 | C22⋊C4 | semidirect |
| 128. C2×#104 | D29 | semidirect |
| 160. C29 | #1883 | semidirect |
| 208. Q8 | #90781 | semidirect |
| 216. D4 | #90781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| #14271646 | 2 |
| #14271169 | 2 |
| #14271065 | 2 |
| #14270931 | 2 |
| #14270923 | 2 |
| C2×C29×#104 | 2 |
| #1883 | 29 |