Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#261 |
| commutator, socle | C22×C13 | C23×C4 |
| Fitting | C13×#125 | C4 |
| prime radical | #88149 | C4 |
| cosocle | C2×Dic13 | C24 |
| hypercenter | #125 | #261 |
| hypocenter | C13 | #2967 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11719078 | C2 | semidirect |
| 3. #11719077 | C2 | semidirect |
| 4. #11719076 | C2 | semidirect |
| 5. #11719075 | C2 | semidirect |
| 6. #11719075 | C2 | semidirect |
| 7. #11719072 | C2 | semidirect |
| 8. #11719055 | C2 | semidirect |
| 9. C4×#6118 | C2 | semidirect |
| 178. C13 | #2967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719396 | 2 |
| #11719078 | 2 |
| #11719077 | 2 |
| #11719076 | 2 |
| #11719075 | 2 |
| #11719072 | 2 |
| #11719055 | 2 |
| C4×#6118 | 2 |
| #2967 | 13 |