Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×#67 |
| commutator, cosocle | C3×C4 | C24 |
| Frattini | C4 | C23×D3 |
| Fitting | C3×2−1+4 | C2 |
| socle | C2×C3 | C22×D4 |
| hypercenter | 2−1+4 | D3 |
| hypocenter | C3 | #578 |
| LCS | G ▷ C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×2−1+4 | C2 | semidirect |
| 2. #1010 | C2 | semidirect |
| 3. #951 | C2 | semidirect |
| 4. #950 | C2 | semidirect |
| 5. #948 | C2 | semidirect |
| 6. C2×#216 | C2 | semidirect |
| 7. #942 | C2 | semidirect |
| 26. 2−1+4 | D3 | semidirect |
| 100. C3 | #578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×2−1+4 | 2 |
| #1010 | 2 |
| #951 | 2 |
| #950 | 2 |
| #948 | 2 |
| C2×#216 | 2 |
| #942 | 2 |
| #578 | 3 |