Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
828 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C4×#10624382 | C2 | semidirect |
| 3. C2×(C2×#10624382)⋊C4 | C2 | semidirect |
| 4. C2×(C2×#10624382)⋊C4 | C2 | semidirect |
| 10. C2×C22⋊#10624382 | C4 | semidirect |
| 18. C2×C22⋊Dic181 | C4 | semidirect |
| 19. C2×#15668426 | C4 | semidirect |
| 20. C2×#15668426 | C4 | semidirect |
| 23. C2×C22⋊C4×C181 | C4 | semidirect |
| 80. C2×#10624382 | C22⋊C4 | semidirect |
| 101. C22×D181 | C42 | semidirect |
| 113. C2×Dic181 | C22⋊C4 | semidirect |
| 124. C23×C181 | C42 | semidirect |
| 129. C2×C4×C181 | C22⋊C4 | semidirect |
| 182. C181 | #1437 | semidirect |
| 202. C2×C22⋊C4 | #10624382 | semidirect |
| 283. C23 | C4×#10624382 | semidirect |
| 312. C2×C4 | C22⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10624382 | 2 |
| C22×C4×#10624382 | 2 |
| C2×(C2×#10624382)⋊C4 | 2 |
| C2×C22⋊C4×D181 | 2 |
| #1437 | 181 |