Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #26012538 | C2 | semidirect |
| 2. #26012532 | C2 | semidirect |
| 3. #26012415 | C2 | semidirect |
| 4. #26012409 | C2 | semidirect |
| 5. #26012407 | C2 | semidirect |
| 6. #26012381 | C2 | semidirect |
| 18. #19149624 | C4 | semidirect |
| 19. #19149623 | C4 | semidirect |
| 20. #19149620 | C4 | semidirect |
| 22. D16×C173 | C4 | semidirect |
| 34. Dic692 | C2×C4 | semidirect |
| 39. #14583801 | C2×C4 | semidirect |
| 41. D8×C173 | C2×C4 | semidirect |
| 42. C16×C173 | C2×C4 | semidirect |
| 75. C173 | AGL(1,ℤ/16) | semidirect |
| 91. D16 | #10621924 | semidirect |
| 107. D8 | C2×#10621924 | semidirect |
| 118. C16 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012538 | 2 |
| #26012532 | 2 |
| #26012415 | 2 |
| #26012409 | 2 |
| #26012407 | 2 |
| #26012381 | 2 |
| #26011925 | 2 |
| AGL(1,ℤ/16) | 173 |