Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
1072 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#10596842 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C2 | C23×#10596842 |
| Fitting | C24×C73 | C8 |
| socle | C23×C73 | C2×C8 |
| hypercenter | C24 | #10596842 |
| hypocenter | C73 | C22×C22⋊C8 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C24 | |
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 | direct (N × H) |
| 5. C22×#10596842 | C22 | semidirect |
| 6. C22⋊#10596842 | C22 | direct (N × H) |
| 14. C2×#10596842 | C23 | semidirect |
| 26. C23×D73 | C8 | semidirect |
| 27. C23×D73 | C8 | semidirect |
| 30. C24×C73 | C8 | semidirect |
| 33. C23×C73 | C2×C8 | semidirect |
| 40. C22×D73 | C2×C8 | semidirect |
| 41. C22×D73 | C2×C8 | semidirect |
| 55. C22×C73 | C22⋊C8 | semidirect |
| 57. C22×C73 | C22×C8 | semidirect |
| 62. C2×D73 | C22⋊C8 | semidirect |
| 65. C2×D73 | C22×C8 | semidirect |
| 72. C2×C73 | C2×C22⋊C8 | semidirect |
| 75. D73 | C2×C22⋊C8 | semidirect |
| 79. C73 | C22×C22⋊C8 | semidirect |
| 98. C24 | #10596842 | semidirect |
| 123. C23 | C2×#10596842 | semidirect |
| 144. C22 | C22⋊#10596842 | direct (N × H) |
| 146. C22 | C22×#10596842 | semidirect |
| 155. C2 | C2×C22⋊#10596842 | direct (N × H) |