Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#10596842 |
| commutator, socle | C2×C73 | C2×C4×C8 |
| Fitting | M16×C73 | C8 |
| hypercenter | M16 | #10596842 |
| hypocenter | C73 | C8×M16 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #17989671 | C2 | semidirect |
| 4. C8×#10596842 | C2 | semidirect |
| 24. #11924038 | C8 | semidirect |
| 25. #11924037 | C8 | semidirect |
| 32. #11924012 | C8 | semidirect |
| 33. #11924011 | C8 | semidirect |
| 35. M16×C73 | C8 | semidirect |
| 45. #10596842 | M16 | direct (N × H) |
| 52. #10596833 | C2×C8 | semidirect |
| 53. C8×C73 | C2×C8 | semidirect |
| 54. #10596831 | C2×C8 | semidirect |
| 74. C73 | C8×M16 | semidirect |
| 99. M16 | #10596842 | direct (N × H) |
| 128. C8 | C2×#10596842 | semidirect |