Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 398 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 | #393 |
| commutator, Frattini, cosocle | C2×C42 | C23×C73 |
| prime radical | #532×C73 | C22 |
| 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 |
|---|---|---|
| 1. C73×#2605 | C2 | semidirect |
| 5. C73×#1300 | C2 | semidirect |
| 6. C73×#1288 | C2 | semidirect |
| 7. C73×#1285 | C2 | semidirect |
| 30. C4⋊Q8×C73 | Q8 | semidirect |
| 31. #127×C73 | Q8 | semidirect |
| 175. #10378 | C73 | direct (N × H) |
| 182. #2605 | C2×C73 | semidirect |
| 186. #1300 | C2×C73 | semidirect |
| 187. #1288 | C2×C73 | semidirect |
| 188. #1285 | C2×C73 | semidirect |
| 189. C73 | #10378 | direct (N × H) |
| 212. C4⋊Q8 | Q8×C73 | semidirect |
| 213. #127 | Q8×C73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#2605 | 2 |
| C73×#1980 | 2 |
| C73×#1514 | 2 |
| C73×#1505 | 2 |
| C73×#1300 | 2 |
| C73×#1288 | 2 |
| C73×#1285 | 2 |
| #10378 | 73 |