Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 126 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 | #410 |
| commutator | C22×C4 | C22×C4×C73 |
| Frattini, cosocle | C2×#41 | C23×C73 |
| socle | C2×C73 | #1799 |
| prime radical | #532×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C2×C8×C73 ◁ C2×#131×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C73×#1813 | C2 | semidirect |
| 4. C73×#1392 | C2 | semidirect |
| 127. #12809 | C73 | direct (N × H) |
| 135. #1813 | C2×C73 | semidirect |
| 136. #1392 | C2×C73 | semidirect |
| 137. C73 | #12809 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#2931 | 2 |
| C73×#2132 | 2 |
| C73×#1813 | 2 |
| C73×#1392 | 2 |
| #12809 | 73 |