Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
864 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C73 | #120 |
| commutator | C24 | C22×C4×C73 |
| Frattini, cosocle | C23×C4 | C23×C73 |
| socle | C22×C73 | #379 |
| prime radical | C73×#3459 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C73 ◁ C23×C4×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C73×#1869 | C2 | semidirect |
| 3. C73×#1459 | C2 | semidirect |
| 138. #8317 | C73 | direct (N × H) |
| 146. #1869 | C2×C73 | semidirect |
| 147. #1459 | C2×C73 | semidirect |
| 148. C73 | #8317 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#3459 | 2 |
| C73×#1869 | 2 |
| C73×#1459 | 2 |
| #8317 | 73 |