Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1068 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 237 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 | C24×C4×C13 | C2 |
| prime radical | C25×C13 | C22 |
| hypercenter | C24×C4 | D13 |
| hypocenter | C13 | #2848 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#88178 | C2 | semidirect |
| 4. #11718873 | C2 | semidirect |
| 5. #11718871 | C2 | semidirect |
| 10. C22×Dic26 | C22 | semidirect |
| 13. C2×C4⋊Dic13 | C22 | semidirect |
| 15. C2×#6101 | C22 | semidirect |
| 16. #88071 | C22 | semidirect |
| 19. C24×C13 | Q8 | semidirect |
| 64. C22×C13 | C22⋊Q8 | semidirect |
| 89. C24 | Dic26 | semidirect |
| 105. C13 | #2848 | semidirect |
| 129. C22 | #88178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C13 | 2 |
| C2×#88178 | 2 |
| #11718908 | 2 |
| #11718873 | 2 |
| #11718871 | 2 |
| #2848 | 13 |