Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26015040 | C2 | semidirect |
| 2. #26015024 | C2 | semidirect |
| 3. #26015023 | C2 | semidirect |
| 4. #26015015 | C2 | semidirect |
| 5. #26015014 | C2 | semidirect |
| 6. Q16×D353 | C2 | semidirect |
| 7. #26014998 | C2 | semidirect |
| 8. C2×Q16×C353 | C2 | semidirect |
| 59. C353 | #578 | semidirect |
| 67. C2×Q16 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26015040 | 2 |
| #26015024 | 2 |
| #26015023 | 2 |
| #26015015 | 2 |
| #26015014 | 2 |
| Q16×D353 | 2 |
| #26014998 | 2 |
| C2×Q16×C353 | 2 |
| #578 | 353 |