Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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, cosocle | C23×C13 | C24 |
| Fitting | C13×#391 | C2 |
| prime radical | C22×D52 | C22 |
| hypercenter | #391 | D13 |
| hypocenter | C13 | #2804 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#391 | C2 | semidirect |
| 2. #11718892 | C2 | semidirect |
| 3. #11718650 | C2 | semidirect |
| 5. #11718590 | C2 | semidirect |
| 6. #11718334 | C2 | semidirect |
| 7. #11718329 | C2 | semidirect |
| 9. #11718321 | C2 | semidirect |
| 45. C2×D52 | Q8 | semidirect |
| 103. #391 | D13 | semidirect |
| 190. C13 | #2804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#391 | 2 |
| #11718892 | 2 |
| #11718650 | 2 |
| #11718600 | 2 |
| #11718590 | 2 |
| #11718334 | 2 |
| #11718329 | 2 |
| #11718326 | 2 |
| #11718321 | 2 |
| #2804 | 13 |