Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
872 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 275 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. C2×Q8×Dic29 | C2 | semidirect |
| 3. #14271065 | C2 | semidirect |
| 4. #14271064 | C2 | semidirect |
| 5. #14271020 | C2 | semidirect |
| 6. C4×#90781 | C2 | semidirect |
| 7. C2×C4×Q8×C29 | C2 | semidirect |
| 11. C2×#90809 | C4 | semidirect |
| 57. Q8×C29 | C22⋊C4 | semidirect |
| 66. C2×C4×C29 | #41 | semidirect |
| 75. C2×Dic29 | #41 | semidirect |
| 101. C2×C4×Q8 | D29 | semidirect |
| 131. C29 | #2341 | semidirect |
| 164. Q8 | #90781 | semidirect |
| 183. C2×C4 | #90809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90809 | 2 |
| C2×Q8×Dic29 | 2 |
| #14271065 | 2 |
| #14271064 | 2 |
| #14271020 | 2 |
| C4×#90781 | 2 |
| C2×C4×Q8×C29 | 2 |
| #2341 | 29 |