Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
408 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 121 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×C4 | C22×D73 |
| commutator, socle | C23×C73 | C22×C4 |
| Fitting | C2×C4×D4×C73 | C2 |
| hypercenter | C2×C4×D4 | D73 |
| hypocenter | C73 | #1870 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11924012 | C2 | semidirect |
| 2. C2×C22⋊#10596831 | C2 | semidirect |
| 3. C2×C22⋊#10596831 | C2 | semidirect |
| 4. #17988342 | C2 | semidirect |
| 27. C2×#10596831 | D4 | semidirect |
| 60. C23×C73 | M16 | semidirect |
| 77. C2×C4×C73 | M16 | semidirect |
| 114. C73 | #1870 | semidirect |
| 174. C23 | #11924012 | semidirect |
| 191. C2×C4 | #11924012 | semidirect |