Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
224 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#64408 |
| commutator | C2×C73 | C2×C4×C8 |
| Fitting | C4⋊C8×C73 | C4 |
| socle | C22×C73 | C2×C42 |
| hypercenter | C4⋊C8 | #64408 |
| hypocenter | C73 | C8×M16 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #17989429 | C2 | semidirect |
| 4. C8×#10596833 | C2 | semidirect |
| 18. #11924038 | C8 | semidirect |
| 44. #10596833 | C2×C8 | semidirect |
| 45. #10596833 | M16 | semidirect |
| 64. C73 | C8×M16 | semidirect |