Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×C22⋊D97 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | C4×Q8×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | C4×Q8 | D97 |
| hypocenter | C97 | #440 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #15690743 | C2 | semidirect |
| 4. #15690734 | C2 | semidirect |
| 6. #15690721 | C2 | semidirect |
| 7. C4×Q8×C97 | C2 | semidirect |
| 10. #13095498 | C4 | semidirect |
| 22. Q8×C97 | C2×C4 | semidirect |
| 33. #11715895 | C2×C4 | semidirect |
| 49. C97 | #440 | semidirect |
| 52. C4×Q8 | D97 | semidirect |
| 72. Q8 | C4×D97 | semidirect |