Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D97 |
| commutator, socle | C22×C97 | C22×C4 |
| Fitting | C2×M16×C97 | C2 |
| hypercenter | C2×M16 | D97 |
| hypocenter | C97 | #436 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13095494 | C2 | semidirect |
| 3. #15690739 | C2 | semidirect |
| 4. C22⋊#11715895 | C2 | semidirect |
| 5. #15690722 | C2 | semidirect |
| 6. C8×Dic97 | C2 | semidirect |
| 7. C2×M16×C97 | C2 | semidirect |
| 34. C8×C97 | D4 | semidirect |
| 49. Dic97 | M16 | semidirect |
| 55. C97 | #436 | semidirect |
| 58. C2×M16 | D97 | semidirect |
| 92. C8 | C22⋊D97 | semidirect |