Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
588 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 210 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 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | C4⋊Q8×C73 | C4 |
| hypercenter | C4⋊Q8 | #64408 |
| hypocenter | C73 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 19. #14556591 | C4 | semidirect |
| 20. #14556590 | C4 | semidirect |
| 21. #14556589 | C4 | semidirect |
| 24. C4⋊Q8×C73 | C4 | semidirect |
| 36. C4×#64408 | Q8 | semidirect |
| 84. #64408 | C4⋊Q8 | direct (N × H) |
| 87. C4×C73 | C4×Q8 | semidirect |
| 90. Dic73 | C4×Q8 | semidirect |
| 97. C73 | C4×C4⋊Q8 | semidirect |
| 109. C4⋊Q8 | #64408 | direct (N × H) |
| 187. C4 | Q8×#64408 | semidirect |