Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 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×#393 | C2 |
| hypercenter | #393 | D13 |
| hypocenter | C13 | #2388 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6131 | C2 | semidirect |
| 2. C2×#88135 | C2 | semidirect |
| 3. C13×#393 | C2 | semidirect |
| 4. #11718890 | C2 | semidirect |
| 5. #11718621 | C2 | semidirect |
| 6. #11718333 | C2 | semidirect |
| 7. #11718327 | C2 | semidirect |
| 38. C2×C4×D13 | D4 | semidirect |
| 47. C23×C13 | #41 | semidirect |
| 65. C2×Dic13 | #41 | semidirect |
| 72. #393 | D13 | semidirect |
| 132. C13 | #2388 | semidirect |
| 140. C23 | #6131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6131 | 2 |
| C2×#88135 | 2 |
| C13×#393 | 2 |
| #11718890 | 2 |
| #11718621 | 2 |
| #11718333 | 2 |
| #11718327 | 2 |
| #2388 | 13 |