Finite Group DatabasebetaFinite Group DatabasebetaOrder 8384.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D131 |
| commutator, socle | C22×C131 | C24 |
| Fitting | #123×C131 | C2 |
| hypercenter | #123 | D131 |
| hypocenter | C131 | #560 |
| LCS | G ▷ C22×C131 ▷ C131 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16862242 | C2 | semidirect |
| 2. #16862241 | C2 | semidirect |
| 3. #16862228 | C2 | semidirect |
| 4. #16862221 | C2 | semidirect |
| 5. #16862220 | C2 | semidirect |
| 6. #16862219 | C2 | semidirect |
| 7. #16862216 | C2 | semidirect |
| 8. #16862214 | C2 | semidirect |
| 9. #123×C131 | C2 | semidirect |
| 13. C2×D524 | C22 | semidirect |
| 16. C2×C22⋊D131 | C22 | semidirect |
| 17. C2×C4×D131 | C22 | semidirect |
| 18. C4⋊Dic131 | C22 | semidirect |
| 19. Dic131⋊C4 | C22 | semidirect |
| 24. (C2×D131)⋊C4 | C22 | semidirect |
| 25. C4×Dic131 | C22 | semidirect |
| 27. C22×C4×C131 | C22 | semidirect |
| 28. C4⋊C4×C131 | C22 | semidirect |
| 30. C22⋊C4×C131 | C22 | semidirect |
| 74. C131 | #560 | semidirect |
| 79. #123 | D131 | semidirect |
| 94. C22×C4 | C2×D131 | semidirect |
| 97. C4⋊C4 | C2×D131 | semidirect |
| 104. C22⋊C4 | C2×D131 | semidirect |