Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
336 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C73 |
| Frattini, cosocle | C22×C4 | C23×C73 |
| prime radical | C24×C73 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C23×C4×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #328×C73 | C2 | direct (N × H) |
| 5. C22×Q8×C73 | C4 | semidirect |
| 11. C22⋊Q8×C73 | C4 | semidirect |
| 14. C2×C4⋊C4×C73 | C4 | semidirect |
| 23. C2×Q8×C73 | C2×C4 | semidirect |
| 42. C4⋊C4×C73 | C2×C4 | semidirect |
| 96. C2×C73 | #328 | direct (N × H) |
| 100. C2×#328 | C73 | direct (N × H) |
| 101. C73 | C2×#328 | direct (N × H) |
| 105. #328 | C2×C73 | direct (N × H) |
| 106. C22×Q8 | C4×C73 | semidirect |
| 112. C22⋊Q8 | C4×C73 | semidirect |
| 115. C2×C4⋊C4 | C4×C73 | semidirect |
| 124. C2×Q8 | C2×C4×C73 | semidirect |
| 143. C4⋊C4 | C2×C4×C73 | semidirect |
| 197. C2 | #328×C73 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊Q8×C73 | 2 |
| C2×C22⋊C8×C73 | 2 |
| C2×#95×C73 | 2 |
| #328×C73 | 2 |
| C2×#328 | 73 |