Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 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 | C2×C22⋊D97 |
| commutator | C2×C4×C97 | C23 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #121×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | #121 | D97 |
| hypocenter | C97 | #465 |
| LCS | G ▷ C2×C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13095499 | C2 | semidirect |
| 2. C22×#11715895 | C2 | semidirect |
| 3. #15690789 | C2 | semidirect |
| 4. #15690741 | C2 | semidirect |
| 5. #15690733 | C2 | semidirect |
| 6. #15690731 | C2 | semidirect |
| 36. #11715895 | D4 | semidirect |
| 42. C22×C97 | SD16 | semidirect |
| 55. C97 | #465 | semidirect |
| 98. C22 | #13095499 | semidirect |