Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1088 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 197 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, prime radical | C23×D4×C13 | C2 |
| hypercenter | C23×D4 | D13 |
| hypocenter | C13 | #2435 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#88190 | C2 | semidirect |
| 3. C2×#88178 | C2 | semidirect |
| 4. #11718908 | C2 | semidirect |
| 5. #11718883 | C2 | semidirect |
| 6. #11718882 | C2 | semidirect |
| 7. C4×C22⋊Dic13 | C2 | semidirect |
| 14. C22×Dic26 | C22 | semidirect |
| 17. C2×C22⋊Dic13 | C22 | semidirect |
| 18. C2×C22⋊Dic13 | C22 | semidirect |
| 20. C2×C4⋊Dic13 | C22 | semidirect |
| 22. C2×#6101 | C22 | semidirect |
| 23. C2×C4×Dic13 | C22 | semidirect |
| 24. #88071 | C22 | semidirect |
| 99. C22×C13 | #124 | semidirect |
| 160. C13 | #2435 | semidirect |
| 199. C22 | #88190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D4×C13 | 2 |
| C2×#88190 | 2 |
| C2×#88178 | 2 |
| #11718908 | 2 |
| #11718883 | 2 |
| #11718882 | 2 |
| C4×C22⋊Dic13 | 2 |
| #2435 | 13 |