Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C73 |
| prime radical | C22×D4×C73 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C73×#1569 | C2 | semidirect |
| 4. C73×#1559 | C2 | semidirect |
| 6. C73×#1526 | C2 | semidirect |
| 7. C73×#1291 | C2 | semidirect |
| 175. #10498 | C73 | direct (N × H) |
| 183. #1569 | C2×C73 | semidirect |
| 184. #1559 | C2×C73 | semidirect |
| 186. #1526 | C2×C73 | semidirect |
| 187. #1291 | C2×C73 | semidirect |
| 188. C73 | #10498 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#3215 | 2 |
| C73×#1967 | 2 |
| C73×#1569 | 2 |
| C73×#1559 | 2 |
| C73×#1527 | 2 |
| C73×#1526 | 2 |
| C73×#1291 | 2 |
| #10498 | 73 |