Order 18688.
1278 conjugacy classes of subgroups.
The subgroup lattice has 410 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D73 |
| commutator | C23×C73 | C23×C4 |
| Fitting | C73×#1434 | C2 |
| socle, prime radical, cosocle | C24×C73 | C24 |
| hypercenter | #1434 | D73 |
| hypocenter | C73 | #14690 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ #1434 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 23. C42×Dic73 | C4 | semidirect |
| 214. C73 | #14690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×Dic73 | 2 |
| #22608158 | 2 |
| #22608157 | 2 |
| #22608156 | 2 |
| #22608155 | 2 |
| C73×#1434 | 2 |
| #14690 | 73 |