Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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×#383 | C2 |
| socle, cosocle | C23×C13 | C24 |
| prime radical | C22×D52 | C22 |
| hypercenter | #383 | D13 |
| hypocenter | C13 | #2337 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#383 | C2 | semidirect |
| 3. C4×C4⋊Dic13 | C2 | semidirect |
| 4. #11718331 | C2 | semidirect |
| 5. #11718330 | C2 | semidirect |
| 6. #11718329 | C2 | semidirect |
| 7. #11718327 | C2 | semidirect |
| 9. #11718307 | C2 | semidirect |
| 24. #88129 | C4 | semidirect |
| 47. C2×Dic26 | C2×C4 | semidirect |
| 48. C42×C13 | C2×C4 | semidirect |
| 52. #6103 | C2×C4 | semidirect |
| 53. #6103 | C2×C4 | semidirect |
| 99. #383 | D13 | semidirect |
| 176. C42 | C4×D13 | semidirect |
| 177. C13 | #2337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88129 | 2 |
| C13×#383 | 2 |
| C4×C4⋊Dic13 | 2 |
| #11718331 | 2 |
| #11718330 | 2 |
| #11718329 | 2 |
| #11718327 | 2 |
| #11718326 | 2 |
| #11718307 | 2 |
| #2337 | 13 |