Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
310 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D193 |
| commutator, socle, cosocle | C22×C193 | C24 |
| Frattini | C22 | C23×D193 |
| Fitting | C2×C42×C193 | C2 |
| hypercenter | C2×C42 | D193 |
| hypocenter | C193 | #532 |
| LCS | G ▷ C22×C193 ▷ C193 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15690555 | C2 | semidirect |
| 2. #20259899 | C2 | semidirect |
| 3. #20259896 | C2 | semidirect |
| 4. #20259887 | C2 | semidirect |
| 5. #20259873 | C2 | semidirect |
| 6. C4×D772 | C2 | semidirect |
| 7. C2×C42×C193 | C2 | semidirect |
| 30. C2×C4×C193 | D4 | semidirect |
| 43. C4×C193 | #41 | semidirect |
| 49. C193 | #532 | semidirect |
| 57. C2×C42 | D193 | semidirect |
| 80. C2×C4 | D772 | semidirect |
| 94. C4 | #15690555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690555 | 2 |
| #20259899 | 2 |
| #20259896 | 2 |
| #20259887 | 2 |
| #20259873 | 2 |
| C4×D772 | 2 |
| C2×C42×C193 | 2 |
| #532 | 193 |