Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D3 |
| commutator, socle, cosocle | C22×C3 | C24 |
| Fitting | C22×C3×Q8 | C2 |
| prime radical | C2×#67 | C22 |
| hypercenter | C22×Q8 | D3 |
| hypocenter | C3 | D4×Q8 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×Q8 | C2 | semidirect |
| 2. C2×D3×Q8 | C2 | semidirect |
| 3. #946 | C2 | semidirect |
| 4. Q8×Dic3 | C2 | semidirect |
| 5. #944 | C2 | semidirect |
| 7. #924 | C2 | semidirect |
| 24. C22×Q8 | D3 | semidirect |
| 33. C3×Q8 | D4 | semidirect |
| 37. #67 | Q8 | direct (N × H) |
| 59. C22×C3 | C2×Q8 | semidirect |
| 63. C2×D3 | C2×Q8 | semidirect |
| 68. Dic3 | C2×Q8 | semidirect |
| 73. Q8 | #67 | direct (N × H) |
| 92. C22 | D3×Q8 | semidirect |
| 99. C3 | D4×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q8 | 2 |
| C2×D3×Q8 | 2 |
| #946 | 2 |
| Q8×Dic3 | 2 |
| #944 | 2 |
| C4×#67 | 2 |
| #924 | 2 |
| D4×Q8 | 3 |