Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 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×D97 |
| commutator | C2×C97 | C23×C4 |
| Fitting | C2×C4⋊C4×C97 | C2 |
| socle | C22×C97 | C24 |
| hypercenter | C2×C4⋊C4 | D97 |
| hypocenter | C97 | #520 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15690775 | C2 | semidirect |
| 3. #15690772 | C2 | semidirect |
| 4. C4×C22⋊D97 | C2 | semidirect |
| 5. #15690769 | C2 | semidirect |
| 6. #15690768 | C2 | semidirect |
| 7. C4⋊C4×D97 | C2 | semidirect |
| 8. C2×C4⋊C4×C97 | C2 | semidirect |
| 9. #13095511 | C4 | semidirect |
| 29. C2×C4×C97 | C2×C4 | semidirect |
| 33. C22⋊D97 | C2×C4 | semidirect |
| 37. D388 | C2×C4 | semidirect |
| 39. C4×D97 | C2×C4 | semidirect |
| 40. Dic194 | C2×C4 | semidirect |
| 59. C97 | #520 | semidirect |
| 68. C2×C4⋊C4 | D97 | semidirect |
| 97. C2×C4 | C4×D97 | semidirect |