Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
124 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 124 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.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D3 |
| commutator, socle | C22×C3 | C22×C4 |
| Fitting | C22×C3×C8 | C2 |
| prime radical | C2×#67 | C4 |
| cosocle | C2×C3×C4 | C23 |
| hypercenter | C22×C8 | D3 |
| hypocenter | C3 | #435 |
| 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 |
|---|---|---|
| 1. C22×C3×C8 | C2 | semidirect |
| 3. C2×ΓL(1,𝔽25) | C2 | semidirect |
| 4. #830 | C2 | semidirect |
| 5. (C2×D3)⋊C8 | C2 | semidirect |
| 6. #815 | C2 | semidirect |
| 7. Dic3⋊C8 | C2 | semidirect |
| 23. C22×C8 | D3 | semidirect |
| 42. C3×C8 | D4 | semidirect |
| 60. C22×C3 | M16 | semidirect |
| 86. C8 | #67 | semidirect |
| 97. C22 | ΓL(1,𝔽25) | semidirect |
| 105. C3 | #435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C8 | 2 |
| C4×#67 | 2 |
| C2×ΓL(1,𝔽25) | 2 |
| #830 | 2 |
| (C2×D3)⋊C8 | 2 |
| #815 | 2 |
| Dic3⋊C8 | 2 |
| #435 | 3 |