Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
432 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 91 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 | C2×D4×C73 | C8 |
| hypercenter | C2×D4 | #10596842 |
| hypocenter | C73 | #1869 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#10596842 | C2 | semidirect |
| 2. C2×C22⋊#10596842 | C2 | semidirect |
| 3. C2×C22⋊#10596842 | C2 | semidirect |
| 4. (C2×#10596842)⋊C4 | C2 | semidirect |
| 27. C2×#10596842 | D4 | semidirect |
| 47. C2×D292 | C8 | semidirect |
| 48. C2×C22⋊D73 | C8 | semidirect |
| 49. C2×C22⋊D73 | C8 | semidirect |
| 53. C2×D4×C73 | C8 | semidirect |
| 55. C23×C73 | C2×C8 | semidirect |
| 64. C22×D73 | C2×C8 | semidirect |
| 86. C2×C4×C73 | C2×C8 | semidirect |
| 89. C2×Dic73 | C2×C8 | semidirect |
| 96. C22×C73 | C22⋊C8 | semidirect |
| 107. C2×D73 | C22⋊C8 | semidirect |
| 130. C73 | #1869 | semidirect |
| 158. C2×D4 | #10596842 | semidirect |
| 196. C23 | C2×#10596842 | semidirect |
| 220. C2×C4 | C2×#10596842 | semidirect |
| 240. C22 | C22⋊#10596842 | semidirect |