Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
292 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 115 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, socle | C22×C97 | C24 |
| Fitting | C4×D4×C97 | C2 |
| hypercenter | C4×D4 | D97 |
| hypocenter | C97 | #547 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13095510 | C2 | semidirect |
| 2. #15690810 | C2 | semidirect |
| 3. #15690794 | C2 | semidirect |
| 4. #15690790 | C2 | semidirect |
| 5. #15690784 | C2 | semidirect |
| 6. C4×D388 | C2 | semidirect |
| 7. C2×C4⋊Dic97 | C2 | semidirect |
| 8. C4×D4×C97 | C2 | semidirect |
| 28. D4×C97 | D4 | semidirect |
| 51. C4×C97 | #41 | semidirect |
| 59. C97 | #547 | semidirect |
| 67. C4×D4 | D97 | semidirect |
| 91. D4 | D388 | semidirect |
| 113. C4 | #13095510 | semidirect |