Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
190 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×ΓL(1,𝔽25) | C2 | semidirect |
| 3. #892 | C2 | semidirect |
| 4. C3×#102 | C2 | semidirect |
| 5. #832 | C2 | semidirect |
| 6. #821 | C2 | semidirect |
| 7. #809 | C2 | semidirect |
| 13. D3×D4 | C4 | semidirect |
| 16. C2×C3×C8 | C22 | semidirect |
| 17. C3×C4⋊C4 | C22 | semidirect |
| 19. C4⋊Dic3 | C22 | semidirect |
| 21. C2×C3⋊C8 | C22 | semidirect |
| 29. #102 | D3 | semidirect |
| 58. C2×C8 | C2×D3 | semidirect |
| 60. C4⋊C4 | C2×D3 | semidirect |
| 120. C3 | #418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D4 | 2 |
| C2×ΓL(1,𝔽25) | 2 |
| #892 | 2 |
| C3×#102 | 2 |
| #832 | 2 |
| #821 | 2 |
| #809 | 2 |
| #418 | 3 |