Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
130 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D3×D4 |
| commutator, cosocle | C2×C3×C4 | C23 |
| Frattini | C2×C4 | C22×D3 |
| Fitting | C3×#102 | C2 |
| socle | C22×C3 | C2×D4 |
| hypercenter | #102 | D3 |
| hypocenter | C3 | #469 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #102 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #938 | C2 | semidirect |
| 2. C2×#213 | C2 | semidirect |
| 3. C2×ΓL(1,𝔽25) | C2 | semidirect |
| 4. #895 | C2 | semidirect |
| 5. C3×#102 | C2 | semidirect |
| 6. #821 | C2 | semidirect |
| 7. #808 | C2 | semidirect |
| 28. #102 | D3 | semidirect |
| 45. C3⋊C8 | D4 | semidirect |
| 112. C3 | #469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #938 | 2 |
| C2×#213 | 2 |
| C2×ΓL(1,𝔽25) | 2 |
| #895 | 2 |
| C3×#102 | 2 |
| #821 | 2 |
| #808 | 2 |
| #469 | 3 |