Order 11008.
1258 conjugacy classes of subgroups.
The subgroup lattice has 354 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C43 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C43 |
| Frattini, cosocle | C23×C4 | C23×C43 |
| prime radical | C24×C43 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. C2×#101×C43 | C4 | semidirect |
| 132. C2×C4×C43 | #101 | semidirect |
| 144. #10763 | C43 | direct (N × H) |
| 192. C2×#101 | C4×C43 | semidirect |
| 195. C43 | #10763 | direct (N × H) |
| 309. C2×C4 | #101×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Q8×C43 | 2 |
| C22×#101×C43 | 2 |
| C2×C43×#343 | 2 |
| C43×#1728 | 2 |
| #10763 | 43 |