Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14556561 |
| commutator | C42×C73 | C23 |
| Frattini | C42 | C22×D73 |
| Fitting | Q8⋊C8×C73 | C2 |
| socle | C22×C73 | #120 |
| hypercenter | Q8⋊C8 | D73 |
| hypocenter | C73 | #1651 |
| LCS | G ▷ C42×C73 ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ Q8⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17988985 | C2 | semidirect |
| 3. #17988872 | C2 | semidirect |
| 5. #17988332 | C2 | semidirect |
| 7. Q8⋊C8×C73 | C2 | semidirect |
| 52. Q8×C73 | SD16 | semidirect |
| 93. C73 | #1651 | semidirect |
| 99. Q8⋊C8 | D73 | semidirect |
| 150. Q8 | #11924017 | semidirect |