Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
342 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 119 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×D353 | C2 | semidirect |
| 3. #26014977 | C2 | direct (N × H) |
| 4. C2×#19150716 | C2 | semidirect |
| 5. C2×#19150714 | C2 | semidirect |
| 6. C2×#19150714 | C2 | semidirect |
| 7. C2×#19150714 | C2 | semidirect |
| 8. C2×C4⋊C4×C353 | C2 | semidirect |
| 16. C2×C4×D353 | C22 | semidirect |
| 17. #19150716 | C22 | semidirect |
| 18. #19150714 | C22 | semidirect |
| 19. #19150714 | C22 | semidirect |
| 20. #19150714 | C22 | semidirect |
| 24. C4⋊C4×C353 | C22 | semidirect |
| 63. C2×C353 | #123 | semidirect |
| 69. C353 | C2×#123 | semidirect |
| 75. C2×C4⋊C4 | D353 | semidirect |
| 91. C4⋊C4 | C2×D353 | semidirect |
| 135. C2 | #26014977 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1412 | 2 |
| C22×C4×D353 | 2 |
| #26014977 | 2 |
| C2×#19150716 | 2 |
| C2×#19150714 | 2 |
| C2×C4⋊C4×C353 | 2 |
| C2×#123 | 353 |