Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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 | C22×C73 | C22×C8 |
| Fitting | C2×C22⋊C8×C73 | C2 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C2×C22⋊C8 | D73 |
| hypocenter | C73 | #1954 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14556520 | C2 | semidirect |
| 3. C2×C22⋊#10596831 | C2 | semidirect |
| 4. C2×#14556503 | C2 | semidirect |
| 5. C2×#14556503 | C2 | semidirect |
| 6. C2×C8×Dic73 | C2 | semidirect |
| 7. C2×C22⋊C8×C73 | C2 | semidirect |
| 30. C2×C22⋊D73 | C8 | semidirect |
| 45. C2×#10596831 | D4 | semidirect |
| 65. C2×C8×C73 | D4 | semidirect |
| 140. Dic73 | C22⋊C8 | semidirect |
| 151. C73 | #1954 | semidirect |
| 157. C2×C22⋊C8 | D73 | semidirect |
| 211. C2×C8 | C22⋊D73 | semidirect |