Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 111 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×D3 |
| commutator, socle, cosocle | C22×C3 | C24 |
| Fitting | C22×C3×D4 | C2 |
| hypercenter | C22×D4 | D3 |
| hypocenter | C3 | #534 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×D4 | C2 | semidirect |
| 2. C22×#67 | C2 | semidirect |
| 3. #953 | C2 | semidirect |
| 4. C2×#217 | C2 | semidirect |
| 5. #939 | C2 | semidirect |
| 6. #937 | C2 | semidirect |
| 7. #935 | C2 | semidirect |
| 8. #929 | C2 | semidirect |
| 11. C24×C3 | C22 | semidirect |
| 12. C23×D3 | C22 | semidirect |
| 15. C2×C3×D4 | C22 | semidirect |
| 16. C22×C3×C4 | C22 | semidirect |
| 19. C2×#67 | C22 | semidirect |
| 20. C2×#67 | C22 | semidirect |
| 21. C22×Dic3 | C22 | semidirect |
| 22. C22×Dic3 | C22 | semidirect |
| 23. #217 | C22 | semidirect |
| 24. #217 | C22 | semidirect |
| 25. #217 | C22 | semidirect |
| 26. (C2×D3)⋊C4 | C22 | semidirect |
| 27. Dic3⋊C4 | C22 | semidirect |
| 29. C22×D4 | D3 | semidirect |
| 39. C23×C3 | D4 | semidirect |
| 60. C24 | C2×D3 | semidirect |
| 67. C2×D4 | C2×D3 | semidirect |
| 70. C22×C4 | C2×D3 | semidirect |
| 99. C23 | #67 | semidirect |
| 139. C3 | #534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D4 | 2 |
| C22×#67 | 2 |
| #953 | 2 |
| C2×#217 | 2 |
| #939 | 2 |
| #937 | 2 |
| #935 | 2 |
| #929 | 2 |
| #534 | 3 |