Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#87604 |
| commutator, socle | C22×C97 | C22×C4 |
| Fitting | C4⋊C4×C97 | C4 |
| hypercenter | C4⋊C4 | #87604 |
| hypocenter | C97 | #435 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13095521 | C2 | semidirect |
| 2. C2×#13095519 | C2 | semidirect |
| 3. #15690877 | C2 | semidirect |
| 4. #15690867 | C2 | semidirect |
| 5. #15690867 | C2 | semidirect |
| 6. #15690865 | C2 | semidirect |
| 36. #11715897 | D4 | semidirect |
| 43. C2×D97 | M16 | semidirect |
| 55. C97 | #435 | semidirect |