Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
516 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 165 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 | C43×C13 | C2 |
| prime radical | C22×D52 | C22 |
| hypercenter | C43 | D13 |
| hypocenter | C13 | #2860 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#88130 | C2 | semidirect |
| 2. C43×C13 | C2 | semidirect |
| 3. #11718601 | C2 | semidirect |
| 5. #11718589 | C2 | semidirect |
| 24. C42×C13 | D4 | semidirect |
| 49. C43 | D13 | semidirect |
| 58. C4×C13 | #126 | semidirect |
| 86. C42 | D52 | semidirect |
| 87. C13 | #2860 | semidirect |
| 112. C4 | #88130 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88130 | 2 |
| C43×C13 | 2 |
| #11718601 | 2 |
| #11718600 | 2 |
| #11718589 | 2 |
| #2860 | 13 |