Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1072 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 469 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. C23×#13063436 | C2 | semidirect |
| 2. C2×C22⋊#13063436 | C2 | direct (N × H) |
| 5. C22×#13063436 | C22 | semidirect |
| 6. C22⋊#13063436 | C22 | direct (N × H) |
| 14. C2×#13063436 | C23 | semidirect |
| 17. C24×C173 | C8 | semidirect |
| 35. C23×C173 | C2×C8 | semidirect |
| 50. C22×C173 | C22⋊C8 | semidirect |
| 53. C22×C173 | C22×C8 | semidirect |
| 60. C2×C173 | C2×C22⋊C8 | semidirect |
| 64. C173 | C22×C22⋊C8 | semidirect |
| 80. C24 | #13063436 | semidirect |
| 99. C23 | C2×#13063436 | semidirect |
| 115. C22 | C22⋊#13063436 | direct (N × H) |
| 118. C22 | C22×#13063436 | semidirect |
| 125. C2 | C2×C22⋊#13063436 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13063436 | 2 |
| C2×C22⋊#13063436 | 2 |
| C24×C4×C173 | 2 |
| C22×C22⋊C8 | 173 |