Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
178 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D29 |
| commutator, socle | C22×C29 | C2×C42 |
| Fitting | C29×#431 | C2 |
| prime radical | C23×C29 | C42 |
| cosocle | C42×C29 | C23 |
| hypercenter | #431 | D29 |
| hypocenter | C29 | #1454 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C42 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14270885 | C2 | semidirect |
| 4. #14270885 | C2 | semidirect |
| 5. #14270884 | C2 | semidirect |
| 6. C8×#6597 | C2 | semidirect |
| 85. C29 | #1454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271216 | 2 |
| #14270885 | 2 |
| #14270884 | 2 |
| C8×#6597 | 2 |
| C29×#431 | 2 |
| #1454 | 29 |