Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
3464 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 354 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 |
|---|---|---|
| 1. C22×C22⋊#10624382 | C2 | semidirect |
| 2. #26042220 | C2 | direct (N × H) |
| 4. C23×#10624382 | C22 | semidirect |
| 6. C2×C22⋊#10624382 | C22 | semidirect |
| 8. C24×D181 | C4 | semidirect |
| 9. C24×D181 | C4 | semidirect |
| 12. C25×C181 | C4 | semidirect |
| 14. C22×#10624382 | C23 | semidirect |
| 24. C23×D181 | C2×C4 | semidirect |
| 30. C24×C181 | C2×C4 | semidirect |
| 42. C22×D181 | C22⋊C4 | semidirect |
| 43. C22×D181 | C22⋊C4 | semidirect |
| 52. C23×C181 | C22⋊C4 | semidirect |
| 59. C22×C181 | C2×C22⋊C4 | semidirect |
| 67. C2×D181 | C2×C22⋊C4 | semidirect |
| 72. C2×C181 | #379 | semidirect |
| 75. D181 | #379 | semidirect |
| 77. C181 | C2×#379 | semidirect |
| 87. C25 | #10624382 | semidirect |
| 105. C24 | C2×#10624382 | semidirect |
| 128. C23 | C22⋊#10624382 | semidirect |
| 146. C22 | C2×C22⋊#10624382 | semidirect |
| 153. C2 | #26042220 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10624382 | 2 |
| #26042220 | 2 |
| C25×D181 | 2 |
| C2×#379 | 181 |