Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
630 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 134 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 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C73 |
| Frattini, cosocle | C2×C42 | C23×C73 |
| prime radical | C22×#41×C73 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C22×C42×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C73×#1817 | C2 | semidirect |
| 3. C73×#1272 | C2 | semidirect |
| 4. C73×#1270 | C2 | semidirect |
| 150. #7645 | C73 | direct (N × H) |
| 159. #1817 | C2×C73 | semidirect |
| 160. #1272 | C2×C73 | semidirect |
| 161. #1270 | C2×C73 | semidirect |
| 162. C73 | #7645 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#2297 | 2 |
| C73×#1817 | 2 |
| C73×#1272 | 2 |
| C73×#1270 | 2 |
| #7645 | 73 |