Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D97 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #102×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | #102 | D97 |
| hypocenter | C97 | #416 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #102 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C8×D97 | C2 | semidirect |
| 3. #15690768 | C2 | semidirect |
| 4. #15690735 | C2 | semidirect |
| 5. #15690733 | C2 | semidirect |
| 6. #15690731 | C2 | semidirect |
| 7. #102×C97 | C2 | semidirect |
| 9. #13095510 | C4 | semidirect |
| 57. C97 | #416 | semidirect |
| 65. #102 | D97 | semidirect |