Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
284 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 118 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 | C2×#102 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C4×C8 | C23×C73 |
| prime radical | C23×C73 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ C2×C4×C8×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C73×#1363 | C2 | semidirect |
| 103. #11970 | C73 | direct (N × H) |
| 111. #1363 | C2×C73 | semidirect |
| 112. C73 | #11970 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#3160 | 2 |
| C73×#2163 | 2 |
| C73×#1568 | 2 |
| C73×#1363 | 2 |
| #11970 | 73 |