Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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×#97 | C2 |
| prime radical | C2×D12 | C4 |
| cosocle | C2×C3×C4 | C23 |
| hypercenter | #97 | D3 |
| hypocenter | C3 | #435 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×ΓL(1,𝔽25) | C2 | semidirect |
| 2. C2×D3×C8 | C2 | semidirect |
| 4. C3×#97 | C2 | semidirect |
| 5. (C2×D3)⋊C8 | C2 | semidirect |
| 6. (C2×D3)⋊C8 | C2 | semidirect |
| 7. C4⋊(C3⋊C8) | C2 | semidirect |
| 28. #97 | D3 | semidirect |
| 42. C3×C8 | D4 | semidirect |
| 64. C2×D3 | M16 | semidirect |
| 86. C8 | D12 | semidirect |
| 105. C3 | #435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×ΓL(1,𝔽25) | 2 |
| C2×D3×C8 | 2 |
| C4×D12 | 2 |
| C3×#97 | 2 |
| (C2×D3)⋊C8 | 2 |
| C4⋊(C3⋊C8) | 2 |
| #435 | 3 |