Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
832 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 209 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×#386 | C2 |
| socle, cosocle | C23×C13 | C24 |
| prime radical | C2×#88194 | C2 |
| hypercenter | #386 | D13 |
| hypocenter | C13 | #2366 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×C22⋊D13 | C2 | semidirect |
| 3. C2×#88135 | C2 | semidirect |
| 4. C13×#386 | C2 | semidirect |
| 5. #11718881 | C2 | semidirect |
| 6. #11718618 | C2 | semidirect |
| 7. #11718618 | C2 | semidirect |
| 8. #11718326 | C2 | semidirect |
| 9. #11718310 | C2 | semidirect |
| 21. #88194 | C4 | semidirect |
| 39. C2×D4×C13 | C2×C4 | semidirect |
| 49. C2×C22⋊D13 | C2×C4 | semidirect |
| 50. C2×C22⋊D13 | C2×C4 | semidirect |
| 58. C2×D52 | C2×C4 | semidirect |
| 70. #6101 | D4 | semidirect |
| 73. C4×Dic13 | C2×C4 | semidirect |
| 125. #386 | D13 | semidirect |
| 154. Dic13 | C4×D4 | semidirect |
| 201. C2×D4 | C4×D13 | semidirect |
| 227. C13 | #2366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88194 | 2 |
| C2×C4×C22⋊D13 | 2 |
| C2×#88135 | 2 |
| C13×#386 | 2 |
| #11718881 | 2 |
| #11718618 | 2 |
| #11718326 | 2 |
| #11718310 | 2 |
| #2366 | 13 |