Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
576 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 250 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. #26012495 | C2 | direct (N × H) |
| 3. C2×C4⋊#13063443 | C2 | semidirect |
| 8. C4⋊#13063443 | C22 | semidirect |
| 50. C2×C4×C173 | M16 | semidirect |
| 60. C4×C173 | C2×M16 | semidirect |
| 65. C2×C173 | #423 | semidirect |
| 69. C173 | C2×#423 | semidirect |
| 119. C2×C4 | #14583836 | semidirect |
| 134. C4 | C2×#14583836 | semidirect |
| 136. C2 | #26012495 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583836 | 2 |
| #26012495 | 2 |
| C2×C4⋊#13063443 | 2 |
| C2×C42×D173 | 2 |
| C2×#423 | 173 |