Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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×D131 |
| commutator, socle, cosocle | C23×C131 | C24 |
| Fitting | #381×C131 | C2 |
| prime radical | C24×D131 | C22 |
| hypercenter | #381 | D131 |
| hypocenter | C131 | #2482 |
| LCS | G ▷ C23×C131 ▷ C131 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16862205 | C2 | semidirect |
| 3. #22553249 | C2 | semidirect |
| 4. #22553239 | C2 | semidirect |
| 5. #22553204 | C2 | semidirect |
| 6. #22553187 | C2 | semidirect |
| 8. #381×C131 | C2 | semidirect |
| 12. C2×C4⋊Dic131 | C22 | semidirect |
| 13. C2×C4⋊Dic131 | C22 | semidirect |
| 14. C2×C4⋊Dic131 | C22 | semidirect |
| 21. C2×C4×Dic131 | C22 | semidirect |
| 22. C131⋊#95 | C22 | semidirect |
| 25. #95×C131 | C22 | semidirect |
| 26. #95×C131 | C22 | semidirect |
| 108. C131 | #2482 | semidirect |
| 116. #381 | D131 | semidirect |
| 134. #95 | C2×D131 | semidirect |
| 135. #95 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862205 | 2 |
| C22×(C2×D131)⋊C4 | 2 |
| #22553249 | 2 |
| #22553239 | 2 |
| #22553204 | 2 |
| #22553187 | 2 |
| #22553167 | 2 |
| #381×C131 | 2 |
| #2482 | 131 |