Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
298 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 159 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. C2×#19150721 | C2 | semidirect |
| 3. C2×#19150720 | C2 | semidirect |
| 4. M16×D353 | C2 | direct (N × H) |
| 5. C2×C8×D353 | C2 | semidirect |
| 6. C2×M16×C353 | C2 | semidirect |
| 15. #19150721 | C22 | semidirect |
| 16. #19150720 | C22 | semidirect |
| 17. C2×#15667725 | C22 | semidirect |
| 18. C8×D353 | C22 | semidirect |
| 20. M16×C353 | C22 | semidirect |
| 21. C2×C8×C353 | C22 | semidirect |
| 35. #15667725 | C23 | semidirect |
| 41. C8×C353 | C23 | semidirect |
| 47. C2×D353 | M16 | direct (N × H) |
| 56. C2×C353 | C2×M16 | semidirect |
| 59. D353 | C2×M16 | direct (N × H) |
| 60. C353 | C22×M16 | semidirect |
| 66. C2×M16 | D353 | direct (N × H) |
| 79. M16 | C2×D353 | direct (N × H) |
| 82. C2×C8 | C2×D353 | semidirect |
| 102. C8 | C22×D353 | semidirect |
| 119. C2 | M16×D353 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D353 | 2 |
| C2×#19150721 | 2 |
| C2×#19150720 | 2 |
| M16×D353 | 2 |
| C2×C8×D353 | 2 |
| C2×M16×C353 | 2 |
| C22×M16 | 353 |