Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
190 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D3 |
| commutator, socle | C22×C3 | C22×C4 |
| Fitting | C3×C22⋊C8 | C2 |
| prime radical | C23×D3 | C4 |
| cosocle | C2×C3×C4 | C23 |
| hypercenter | C22⋊C8 | D3 |
| hypocenter | C3 | #407 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C3×C22⋊C8 | C2 | semidirect |
| 4. #830 | C2 | semidirect |
| 5. (C2×D3)⋊C8 | C2 | semidirect |
| 15. C2×C3×C8 | C22 | semidirect |
| 16. C2×C3⋊C8 | C22 | semidirect |
| 22. C22⋊C8 | D3 | semidirect |
| 51. C2×C8 | C2×D3 | semidirect |
| 54. C22×C3 | M16 | semidirect |
| 62. C2×D3 | M16 | semidirect |
| 100. C22 | ΓL(1,𝔽25) | semidirect |
| 106. C3 | #407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D3 | 2 |
| C2×ΓL(1,𝔽25) | 2 |
| C3×C22⋊C8 | 2 |
| #830 | 2 |
| (C2×D3)⋊C8 | 2 |
| #407 | 3 |