Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#10596842 |
| commutator | C4×C73 | C22×C8 |
| Frattini | C4 | C22×#10596842 |
| Fitting | D8×C73 | C8 |
| socle | C2×C73 | C8×D4 |
| hypercenter | D8 | #10596842 |
| hypocenter | C73 | C8×D8 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×#10596842 | C2 | semidirect |
| 2. #17989677 | C2 | semidirect |
| 3. D4⋊#10596842 | C2 | semidirect |
| 4. C8×#10596842 | C2 | semidirect |
| 27. D584 | C8 | semidirect |
| 28. #11924013 | C8 | semidirect |
| 30. D8×C73 | C8 | semidirect |
| 40. #10596842 | D8 | direct (N × H) |
| 41. D4×C73 | C2×C8 | semidirect |
| 43. D292 | C2×C8 | semidirect |
| 46. C8×C73 | C2×C8 | semidirect |
| 47. #10596831 | C2×C8 | semidirect |
| 65. C73 | C8×D8 | semidirect |
| 85. D8 | #10596842 | direct (N × H) |
| 99. D4 | C2×#10596842 | semidirect |
| 112. C8 | C2×#10596842 | semidirect |