Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
192 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 73 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. C8×D116 | C2 | semidirect |
| 3. #14270913 | C2 | semidirect |
| 4. D4⋊#6597 | C2 | semidirect |
| 5. #14270890 | C2 | semidirect |
| 6. #14270885 | C2 | semidirect |
| 7. C8×D4×C29 | C2 | semidirect |
| 34. #90782 | C8 | semidirect |
| 45. D4×C29 | C2×C8 | semidirect |
| 54. D116 | C2×C8 | semidirect |
| 63. #6597 | C2×C8 | semidirect |
| 81. C8×D4 | D29 | semidirect |
| 106. C29 | #1580 | semidirect |
| 131. D4 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#90782 | 2 |
| C8×D116 | 2 |
| #14270913 | 2 |
| D4⋊#6597 | 2 |
| #14270890 | 2 |
| #14270885 | 2 |
| C8×D4×C29 | 2 |
| #1580 | 29 |