Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
734 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 206 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×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C22×D4×C73 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ #376×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C73×#2645 | C2 | semidirect |
| 3. C73×#2043 | C2 | semidirect |
| 5. C73×#2016 | C2 | semidirect |
| 7. C73×#1840 | C2 | semidirect |
| 127. #32805 | C73 | direct (N × H) |
| 133. #2645 | C2×C73 | semidirect |
| 134. #2043 | C2×C73 | semidirect |
| 136. #2016 | C2×C73 | semidirect |
| 138. #1840 | C2×C73 | semidirect |
| 139. C73 | #32805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#2658 | 2 |
| C73×#2645 | 2 |
| C73×#2043 | 2 |
| C73×#2042 | 2 |
| C73×#2016 | 2 |
| C73×#2015 | 2 |
| C73×#1840 | 2 |
| #32805 | 73 |