Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
400 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 105 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×#10596842 |
| commutator, socle | C22×C73 | C22×C8 |
| Fitting | C22×C4×C73 | C8 |
| hypercenter | C22×C4 | #10596842 |
| hypocenter | C73 | #1797 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊#10596842 | C2 | semidirect |
| 3. (C2×#10596842)⋊C4 | C2 | semidirect |
| 35. C22×Dic73 | C8 | semidirect |
| 38. C2×C4×D73 | C8 | semidirect |
| 39. C2×C4×D73 | C8 | semidirect |
| 42. C22×C4×C73 | C8 | semidirect |
| 83. C22×C73 | C4⋊C8 | semidirect |
| 91. C2×D73 | C4⋊C8 | semidirect |
| 104. C4×C73 | C22⋊C8 | semidirect |
| 106. Dic73 | C22⋊C8 | semidirect |
| 117. C73 | #1797 | semidirect |
| 152. C22×C4 | #10596842 | semidirect |
| 213. C22 | C4⋊#10596842 | semidirect |
| 223. C4 | C22⋊#10596842 | semidirect |