Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
226 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 61 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×#11745176 | C2 | semidirect |
| 3. #14270967 | C2 | semidirect |
| 4. C22⋊#90768 | C2 | semidirect |
| 5. C22×Q16×C29 | C2 | semidirect |
| 27. Q16×C29 | D4 | semidirect |
| 55. C22×C29 | SD32 | semidirect |
| 65. C22×Q16 | D29 | semidirect |
| 86. C29 | #2185 | semidirect |
| 97. Q16 | C22⋊D29 | semidirect |
| 127. C22 | #11745176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745176 | 2 |
| #14271399 | 2 |
| #14270967 | 2 |
| C22⋊#90768 | 2 |
| C22×Q16×C29 | 2 |
| #2185 | 29 |