Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D388 |
| commutator | C4×C97 | C24 |
| Frattini | C4 | C23×D97 |
| Fitting | C2×M16×C97 | C2 |
| socle | C2×C97 | C22×D4 |
| hypercenter | C2×M16 | D97 |
| hypocenter | C97 | #575 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13095511 | C2 | semidirect |
| 2. #15690843 | C2 | semidirect |
| 3. #15690838 | C2 | semidirect |
| 4. #15690832 | C2 | semidirect |
| 5. C2×M16×C97 | C2 | semidirect |
| 9. #13095511 | C22 | semidirect |
| 10. C2×Dic194 | C22 | semidirect |
| 11. C2×D388 | C22 | semidirect |
| 14. Dic388 | C22 | semidirect |
| 15. #13095500 | C22 | semidirect |
| 16. D776 | C22 | semidirect |
| 18. M16×C97 | C22 | semidirect |
| 19. C2×C8×C97 | C22 | semidirect |
| 49. C97 | #575 | semidirect |
| 55. C2×M16 | D97 | semidirect |
| 68. M16 | C2×D97 | semidirect |
| 69. C2×C8 | C2×D97 | semidirect |