Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D3×D4 |
| commutator, cosocle | C3×C4 | C24 |
| Frattini | C4 | C23×D3 |
| Fitting | C2×C3×Q16 | C2 |
| socle | C2×C3 | C22×D4 |
| hypercenter | C2×Q16 | D3 |
| hypocenter | C3 | #578 |
| LCS | G ▷ C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×Q16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #1007 | C2 | semidirect |
| 2. C2×C3×Q16 | C2 | semidirect |
| 3. #942 | C2 | semidirect |
| 4. #919 | C2 | semidirect |
| 5. #918 | C2 | semidirect |
| 6. D3×Q16 | C2 | semidirect |
| 7. #904 | C2 | semidirect |
| 8. #901 | C2 | semidirect |
| 35. C2×Q16 | D3 | semidirect |
| 114. C3 | #578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1007 | 2 |
| C2×C3×Q16 | 2 |
| #942 | 2 |
| #919 | 2 |
| #918 | 2 |
| D3×Q16 | 2 |
| #904 | 2 |
| #901 | 2 |
| #578 | 3 |