Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
440 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 215 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×#10596842 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C2 | C23×#10596842 |
| Fitting | C2×Q8×C73 | C8 |
| socle | C22×C73 | C22×C8 |
| hypercenter | C2×Q8 | #10596842 |
| hypocenter | C73 | C2×C8×Q8 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#10596842 | C2 | direct (N × H) |
| 15. C2×#10596842 | Q8 | direct (N × H) |
| 23. C2×Dic146 | C8 | semidirect |
| 24. Q8×D73 | C8 | semidirect |
| 27. C2×Q8×C73 | C8 | semidirect |
| 36. #10596842 | C2×Q8 | direct (N × H) |
| 37. Q8×C73 | C2×C8 | semidirect |
| 42. Dic146 | C2×C8 | semidirect |
| 54. C2×C73 | C8×Q8 | semidirect |
| 56. D73 | C8×Q8 | semidirect |
| 60. C73 | C2×C8×Q8 | semidirect |
| 77. C2×Q8 | #10596842 | direct (N × H) |
| 90. Q8 | C2×#10596842 | direct (N × H) |
| 117. C2 | Q8×#10596842 | direct (N × H) |