Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
1504 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 770 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×#131 |
| 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×#14556679 | C2 | direct (N × H) |
| 2. C22×#11924038 | C2 | semidirect |
| 3. C22×#11924036 | C2 | semidirect |
| 5. #14556679 | C22 | direct (N × H) |
| 6. C2×#11924038 | C22 | semidirect |
| 7. C2×#11924036 | C22 | semidirect |
| 15. #11924038 | C23 | semidirect |
| 16. #11924036 | C23 | semidirect |
| 40. C22×C73 | #131 | semidirect |
| 47. C2×C73 | C2×#131 | semidirect |
| 51. C73 | C22×#131 | semidirect |
| 93. C22 | #14556679 | direct (N × H) |
| 99. C2 | C2×#14556679 | direct (N × H) |