Order 27392.
942 conjugacy classes of subgroups.
The subgroup lattice has 340 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C107 | #95 |
| commutator | C23 | C2×C42×C107 |
| Frattini, cosocle | C23×C4 | C23×C107 |
| prime radical | C25×C107 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C107 ◁ C24×C4×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C107×#1306 | C2 | direct (N × H) |
| 9. #407×C107 | C4 | semidirect |
| 12. C2×C22⋊C8×C107 | C4 | semidirect |
| 40. C22⋊C8×C107 | C2×C4 | semidirect |
| 160. C2×#1306 | C107 | direct (N × H) |
| 167. C2×C107 | #1306 | direct (N × H) |
| 172. #1306 | C2×C107 | direct (N × H) |
| 173. C107 | C2×#1306 | direct (N × H) |
| 179. #407 | C4×C107 | semidirect |
| 182. C2×C22⋊C8 | C4×C107 | semidirect |
| 210. C22⋊C8 | C2×C4×C107 | semidirect |
| 336. C2 | C107×#1306 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#407×C107 | 2 |
| C2×#381×C107 | 2 |
| C107×#1306 | 2 |
| C2×#1306 | 107 |