Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
440 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 234 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. #14272212 | C2 | direct (N × H) |
| 26. C2×Dic58 | C8 | semidirect |
| 30. C2×#6599 | Q8 | semidirect |
| 53. Dic58 | C2×C8 | semidirect |
| 56. #6599 | C2×Q8 | semidirect |
| 75. C2×C29 | C8×Q8 | semidirect |
| 93. C29 | C2×C8×Q8 | semidirect |
| 141. C2 | #14272212 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272212 | 2 |
| C2×#11745220 | 2 |
| C2×C4⋊#6599 | 2 |
| C2×C4×#6599 | 2 |
| C2×#11745249 | 2 |
| C2×C8×Q8 | 29 |