Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
3694 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 3694 conjugacy classes of subgroups — too many to draw. Only its 827 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C25 |
| Frattini | C23 | C24×D17 |
| Fitting | C2×C17×#376 | C2 |
| hypercenter | C2×#376 | D17 |
| hypocenter | C17 | #34641 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11763359 | C2 | semidirect |
| 2. #14534894 | C2 | semidirect |
| 3. #14534890 | C2 | semidirect |
| 4. #14534886 | C2 | semidirect |
| 5. #14532065 | C2 | semidirect |
| 6. C2×C17×#376 | C2 | semidirect |
| 28. C2×C42×C17 | D4 | semidirect |
| 82. C2×#376 | D17 | semidirect |
| 125. C2×C42 | D68 | semidirect |
| 129. C17 | #34641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763359 | 2 |
| #14534894 | 2 |
| #14534890 | 2 |
| #14534886 | 2 |
| #14532065 | 2 |
| C2×C17×#376 | 2 |
| #34641 | 17 |