Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
328 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26011217 | C2 | direct (N × H) |
| 24. C22×C4×C173 | C8 | semidirect |
| 54. C2×C4×C173 | C2×C8 | semidirect |
| 76. C2×C173 | #324 | semidirect |
| 80. C173 | C2×#324 | semidirect |
| 103. C22×C4 | #13063436 | semidirect |
| 134. C2×C4 | C2×#13063436 | semidirect |
| 157. C2 | #26011217 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13063436 | 2 |
| #26011217 | 2 |
| C22×C4⋊C4×C173 | 2 |
| C2×#324 | 173 |