Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
1664 conjugacy classes of subgroups; only the 850 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 850 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×#64408 |
| commutator | C2×C73 | C24×C4 |
| Frattini | C2 | C24×#64408 |
| Fitting | C22×Q8×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C22×Q8 | #64408 |
| hypocenter | C73 | C22×C4×Q8 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×#64408 | C2 | direct (N × H) |
| 7. Q8×#64408 | C22 | direct (N × H) |
| 10. C22×Dic146 | C4 | semidirect |
| 11. C2×Q8×D73 | C4 | semidirect |
| 14. C22×Q8×C73 | C4 | semidirect |
| 16. C22×#64408 | Q8 | direct (N × H) |
| 22. C2×Dic146 | C2×C4 | semidirect |
| 23. Q8×D73 | C2×C4 | semidirect |
| 28. C2×Q8×C73 | C2×C4 | semidirect |
| 36. C2×#64408 | C2×Q8 | direct (N × H) |
| 39. Q8×C73 | C22×C4 | semidirect |
| 44. Dic146 | C22×C4 | semidirect |
| 45. C22×C73 | C4×Q8 | semidirect |
| 47. C2×D73 | C4×Q8 | semidirect |
| 53. #64408 | C22×Q8 | direct (N × H) |
| 56. C2×C73 | C2×C4×Q8 | semidirect |
| 58. D73 | C2×C4×Q8 | semidirect |
| 62. C73 | C22×C4×Q8 | semidirect |
| 70. C22×Q8 | #64408 | direct (N × H) |
| 81. C2×Q8 | C2×#64408 | direct (N × H) |
| 98. Q8 | C22×#64408 | direct (N × H) |
| 112. C22 | Q8×#64408 | direct (N × H) |
| 121. C2 | C2×Q8×#64408 | direct (N × H) |