Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
296 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 6. #19149740 | C4 | direct (N × H) |
| 69. C4×C173 | #101 | semidirect |
| 79. C173 | C4×#101 | semidirect |
| 153. C4 | #19149740 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149740 | 2 |
| C4×#14583835 | 2 |
| #26012371 | 2 |
| C2×C4×Dic346 | 2 |
| C4×#101 | 173 |