Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
198 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 45 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 | C2×C4×C97 | C23 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | C2×D8×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | C2×D8 | D97 |
| hypocenter | C97 | #447 |
| LCS | G ▷ C2×C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×D97 | C2 | semidirect |
| 2. C2×#13095496 | C2 | semidirect |
| 3. #15690781 | C2 | semidirect |
| 4. #15690732 | C2 | semidirect |
| 5. #15690731 | C2 | semidirect |
| 6. #15690722 | C2 | semidirect |
| 7. C2×D8×C97 | C2 | semidirect |
| 16. C2×#11715895 | C22 | semidirect |
| 17. C4⋊Dic97 | C22 | semidirect |
| 20. C2×D4×C97 | C22 | semidirect |
| 22. C2×C8×C97 | C22 | semidirect |
| 33. D4×C97 | D4 | semidirect |
| 40. D388 | D4 | semidirect |
| 58. C2×D97 | D8 | semidirect |
| 70. C97 | #447 | semidirect |
| 74. C2×D8 | D97 | semidirect |
| 86. C2×D4 | C2×D97 | semidirect |
| 91. C2×C8 | C2×D97 | semidirect |
| 108. D4 | C22⋊D97 | semidirect |