Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D97 |
| commutator | C2×C97 | C22×C8 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | C22×C8×C97 | C2 |
| socle | C23×C97 | C2×C4 |
| hypercenter | C22×C8 | D97 |
| hypocenter | C97 | C2×C22⋊C8 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#11715895 | C2 | semidirect |
| 3. #15690722 | C2 | direct (N × H) |
| 4. C22×C8×C97 | C2 | semidirect |
| 12. C2×#11715895 | C22 | semidirect |
| 15. C2×C8×C97 | C22 | semidirect |
| 19. C22×D97 | C8 | semidirect |
| 39. C2×D97 | C2×C8 | semidirect |
| 44. C2×C97 | C22⋊C8 | semidirect |
| 49. C97 | C2×C22⋊C8 | semidirect |
| 53. C22×C8 | D97 | semidirect |
| 65. C2×C8 | C2×D97 | semidirect |
| 95. C2 | #15690722 | direct (N × H) |