Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C73 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C42×C73 ◁ #446×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C73×#3403 | C2 | semidirect |
| 2. C73×#2250 | C2 | semidirect |
| 3. C73×#2206 | C2 | semidirect |
| 4. C73×#1688 | C2 | semidirect |
| 5. C73×#1360 | C2 | semidirect |
| 6. C73×#1338 | C2 | semidirect |
| 7. C73×#1333 | C2 | semidirect |
| 155. #12336 | C73 | direct (N × H) |
| 162. #3403 | C2×C73 | semidirect |
| 163. #2250 | C2×C73 | semidirect |
| 164. #2206 | C2×C73 | semidirect |
| 165. #1688 | C2×C73 | semidirect |
| 166. #1360 | C2×C73 | semidirect |
| 167. #1338 | C2×C73 | semidirect |
| 168. #1333 | C2×C73 | semidirect |
| 169. C73 | #12336 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#3403 | 2 |
| C73×#2250 | 2 |
| C73×#2206 | 2 |
| C73×#1688 | 2 |
| C73×#1360 | 2 |
| C73×#1338 | 2 |
| C73×#1333 | 2 |
| #12336 | 73 |