Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
448 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#102 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C2×#466×C73 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C23×C4×C73 ◁ C23×C8×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C16×C73 | C2 | semidirect |
| 3. C73×#1810 | C2 | semidirect |
| 4. C73×#1349 | C2 | semidirect |
| 18. C22⋊C16×C73 | C22 | semidirect |
| 19. #341×C73 | C22 | semidirect |
| 143. #11891 | C73 | direct (N × H) |
| 152. C2×C22⋊C16 | C2×C73 | semidirect |
| 153. #1810 | C2×C73 | semidirect |
| 154. #1349 | C2×C73 | semidirect |
| 155. C73 | #11891 | direct (N × H) |
| 169. C22⋊C16 | C22×C73 | semidirect |
| 170. #341 | C22×C73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#466×C73 | 2 |
| C2×C22⋊C16×C73 | 2 |
| C73×#1810 | 2 |
| C73×#1349 | 2 |
| #11891 | 73 |