Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
302 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 302 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. #14271203 | C2 | semidirect |
| 4. #14271032 | C2 | semidirect |
| 5. #14270931 | C2 | semidirect |
| 6. #14270924 | C2 | semidirect |
| 23. #11745185 | C4 | semidirect |
| 55. C4×Dic29 | C2×C4 | semidirect |
| 57. #90777 | C2×C4 | semidirect |
| 62. Q8×C29 | C4⋊C4 | semidirect |
| 66. D4×C29 | C4⋊C4 | semidirect |
| 138. C29 | #1859 | semidirect |
| 175. Q8 | #90779 | semidirect |
| 179. D4 | #90779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271646 | 2 |
| #14271203 | 2 |
| C2×#11745185 | 2 |
| #14271032 | 2 |
| #14270931 | 2 |
| #14270924 | 2 |
| C29×#417 | 2 |
| #1859 | 29 |