Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D97 |
| commutator | C22×C97 | C22×C4 |
| Fitting | C2×C22⋊C4×C97 | C2 |
| socle | C23×C97 | C23 |
| hypercenter | C2×C22⋊C4 | D97 |
| hypocenter | C97 | #386 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×Dic97 | C2 | semidirect |
| 3. C2×#13095488 | C2 | semidirect |
| 4. #15690717 | C2 | semidirect |
| 5. C2×C22⋊C4×C97 | C2 | semidirect |
| 9. C2×C22⋊D97 | C4 | semidirect |
| 28. C22×D97 | C2×C4 | semidirect |
| 38. C2×Dic97 | C2×C4 | semidirect |
| 39. C2×Dic97 | D4 | semidirect |
| 44. C22×C97 | C22⋊C4 | semidirect |
| 65. C97 | #386 | semidirect |
| 70. C2×C22⋊C4 | D97 | semidirect |
| 115. C22 | #13095488 | semidirect |