Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 470 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 | #342 |
| commutator | C22×C4 | C42×C73 |
| Frattini, cosocle | C22×#41 | C22×C73 |
| prime radical | C22×#41×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C22×#41×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×#101×C73 | C4 | semidirect |
| 12. C2×C22⋊C8×C73 | C4 | semidirect |
| 131. #7309 | C73 | direct (N × H) |
| 142. C73 | #7309 | direct (N × H) |
| 144. C2×#101 | C4×C73 | semidirect |
| 151. C2×C22⋊C8 | C4×C73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#1785 | 2 |
| C73×#1782 | 2 |
| C73×#1780 | 2 |
| #7309 | 73 |