Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
432 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 217 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. Q8×#6597 | C2 | semidirect |
| 3. C8×D116 | C2 | semidirect |
| 4. #14271228 | C2 | semidirect |
| 5. #14271214 | C2 | semidirect |
| 6. C4⋊C8×D29 | C2 | semidirect |
| 7. C8×Q8×C29 | C2 | semidirect |
| 25. #90809 | C8 | semidirect |
| 43. Q8×C29 | C2×C8 | semidirect |
| 50. D116 | C2×C8 | semidirect |
| 54. C4×D29 | C2×C8 | semidirect |
| 73. C8×Q8 | D29 | semidirect |
| 98. C29 | #2988 | semidirect |
| 118. Q8 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#90809 | 2 |
| Q8×#6597 | 2 |
| C8×D116 | 2 |
| #14271228 | 2 |
| #14271214 | 2 |
| C4⋊C8×D29 | 2 |
| C8×Q8×C29 | 2 |
| #2988 | 29 |