Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11745294 | C2 | semidirect |
| 2. #14271741 | C2 | semidirect |
| 3. C2×#11745185 | C2 | semidirect |
| 4. C2×#11745173 | C2 | semidirect |
| 5. #14271066 | C2 | semidirect |
| 6. #14270931 | C2 | semidirect |
| 7. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 44. C2×D4×C29 | D4 | semidirect |
| 61. M16×C29 | D4 | semidirect |
| 74. #90777 | D4 | semidirect |
| 146. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 183. C29 | #2006 | semidirect |
| 205. C2×D4 | C22⋊D29 | semidirect |
| 218. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| #14271741 | 2 |
| C2×#11745185 | 2 |
| C2×#11745173 | 2 |
| #14271066 | 2 |
| #14270931 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #2006 | 29 |