Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
460 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 170 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×C4⋊Q8 | C4 |
| prime radical, cosocle | C22×D13 | C24 |
| hypercenter | C4⋊Q8 | #261 |
| hypocenter | C13 | #2331 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C13×C4⋊Q8 | C4 | semidirect |
| 15. #88198 | C4 | semidirect |
| 18. #88142 | C4 | semidirect |
| 19. #88142 | C4 | semidirect |
| 21. #88123 | C4 | semidirect |
| 43. C4×#261 | Q8 | semidirect |
| 110. C4⋊Q8 | #261 | semidirect |
| 156. C13 | #2331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×C4⋊Q8 | 2 |
| (C2×#261)⋊Q8 | 2 |
| #11719083 | 2 |
| #11719082 | 2 |
| C4⋊C4×#261 | 2 |
| #11719060 | 2 |
| #11719057 | 2 |
| #2331 | 13 |