Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
496 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 188 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 | #2369 |
| 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 |
|---|---|---|
| 12. C13×C4⋊Q8 | C4 | semidirect |
| 13. #88198 | C4 | semidirect |
| 15. #88142 | C4 | semidirect |
| 17. #88123 | C4 | semidirect |
| 32. C4⋊#261 | Q8 | semidirect |
| 86. C4⋊Q8 | #261 | semidirect |
| 122. C13 | #2369 | 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 |
| C4⋊C4×#261 | 2 |
| C4×C4⋊#261 | 2 |
| #2369 | 13 |