Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
394 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 179 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. #14271242 | C2 | semidirect |
| 4. #14271240 | C2 | semidirect |
| 5. #14271214 | C2 | semidirect |
| 6. #14271185 | C2 | semidirect |
| 7. C8×Q8×C29 | C2 | semidirect |
| 43. Q8×C29 | M16 | semidirect |
| 73. C8×Q8 | D29 | semidirect |
| 98. C29 | #2991 | semidirect |
| 118. Q8 | #90772 | 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 |
| #14271242 | 2 |
| #14271240 | 2 |
| #14271214 | 2 |
| #14271185 | 2 |
| C8×Q8×C29 | 2 |
| #2991 | 29 |