Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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 | C22×C13 | C23×C4 |
| Fitting | C13×#376 | C2 |
| socle, cosocle | C23×C13 | C24 |
| prime radical | C2×#88128 | C2 |
| hypercenter | #376 | D13 |
| hypocenter | C13 | #2328 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×D52 | C2 | semidirect |
| 3. C13×#376 | C2 | semidirect |
| 4. #11718600 | C2 | semidirect |
| 5. #11718597 | C2 | semidirect |
| 6. #11718326 | C2 | semidirect |
| 16. #88128 | C4 | semidirect |
| 29. C2×D52 | C2×C4 | semidirect |
| 30. C2×D52 | C2×C4 | semidirect |
| 34. C42×C13 | C2×C4 | semidirect |
| 35. C42×C13 | D4 | semidirect |
| 65. #376 | D13 | semidirect |
| 115. C42 | C4×D13 | semidirect |
| 116. C42 | D52 | semidirect |
| 117. C13 | #2328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88128 | 2 |
| C2×C4×D52 | 2 |
| C13×#376 | 2 |
| #11718600 | 2 |
| #11718597 | 2 |
| #11718326 | 2 |
| #2328 | 13 |