Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
520 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C73 |
| socle | C2×C73 | #1999 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×C4×C73 ◁ C2×#131×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C73×#3414 | C2 | semidirect |
| 2. C73×#3067 | C2 | semidirect |
| 3. C2×#359×C73 | C2 | semidirect |
| 4. C73×#2113 | C2 | semidirect |
| 5. C73×#1385 | C2 | semidirect |
| 131. #13312 | C73 | direct (N × H) |
| 137. #3414 | C2×C73 | semidirect |
| 138. #3067 | C2×C73 | semidirect |
| 139. C2×#359 | C2×C73 | semidirect |
| 140. #2113 | C2×C73 | semidirect |
| 141. #1385 | C2×C73 | semidirect |
| 142. C73 | #13312 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#3414 | 2 |
| C73×#3067 | 2 |
| C2×#359×C73 | 2 |
| C73×#2113 | 2 |
| C73×#1385 | 2 |
| #13312 | 73 |