Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C24 |
| Frattini | C4 | C23×D97 |
| Fitting | C22×Q8×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | C22×Q8 | D97 |
| hypocenter | C97 | C2×#137 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15690841 | C2 | direct (N × H) |
| 3. C2×#13095501 | C2 | semidirect |
| 4. C2×#13095498 | C2 | semidirect |
| 5. C2×#13095495 | C2 | semidirect |
| 6. C22×Q8×C97 | C2 | semidirect |
| 13. #13095501 | C22 | semidirect |
| 14. #13095498 | C22 | semidirect |
| 15. #13095495 | C22 | semidirect |
| 20. C2×Q8×C97 | C22 | semidirect |
| 53. C2×C97 | #137 | semidirect |
| 56. C97 | C2×#137 | semidirect |
| 59. C22×Q8 | D97 | semidirect |
| 70. C2×Q8 | C2×D97 | semidirect |
| 111. C2 | #15690841 | direct (N × H) |