Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
264 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D73 |
| commutator | C4×C73 | C22×C8 |
| Frattini | C42 | C22×D73 |
| Fitting | Q8⋊C8×C73 | C2 |
| socle | C22×C73 | C2×C22⋊C4 |
| hypercenter | Q8⋊C8 | D73 |
| hypocenter | C73 | #1477 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17988638 | C2 | semidirect |
| 3. C4⋊C8×D73 | C2 | semidirect |
| 4. Q8⋊#10596831 | C2 | semidirect |
| 5. #17988316 | C2 | semidirect |
| 6. #17988314 | C2 | semidirect |
| 7. Q8⋊C8×C73 | C2 | semidirect |
| 28. #11924029 | C8 | semidirect |
| 60. Q8×C73 | C2×C8 | semidirect |
| 72. D292 | C2×C8 | semidirect |
| 110. C73 | #1477 | semidirect |
| 115. Q8⋊C8 | D73 | semidirect |
| 170. Q8 | C8×D73 | semidirect |