Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, prime radical, cosocle | C23×C13 | C24 |
| Fitting | C13×#389 | C2 |
| hypercenter | #389 | D13 |
| hypocenter | C13 | #2734 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 49. C13×C4⋊C4 | Q8 | semidirect |
| 54. C4⋊Dic13 | Q8 | semidirect |
| 168. C4⋊C4 | Dic26 | semidirect |
| 171. C13 | #2734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88142 | 2 |
| C13×#389 | 2 |
| #11718645 | 2 |
| #11718642 | 2 |
| #11718640 | 2 |
| #11718590 | 2 |
| #11718589 | 2 |
| #11718317 | 2 |
| #11718315 | 2 |
| #2734 | 13 |