Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D97 |
| commutator | C4×C97 | C24 |
| Frattini | C4 | C23×D97 |
| Fitting | #135×C97 | C2 |
| socle | C2×C97 | C22×D4 |
| hypercenter | #135 | D97 |
| hypocenter | C97 | #578 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #135 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15690857 | C2 | semidirect |
| 2. #15690840 | C2 | semidirect |
| 3. #15690839 | C2 | semidirect |
| 4. #15690829 | C2 | semidirect |
| 5. C2×Dic388 | C2 | semidirect |
| 6. Q16×D97 | C2 | semidirect |
| 7. #15690816 | C2 | semidirect |
| 8. #135×C97 | C2 | semidirect |
| 59. C97 | #578 | semidirect |
| 65. #135 | D97 | semidirect |