Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
228 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 98 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. #19149750 | C4 | direct (N × H) |
| 53. C4×C173 | #108 | semidirect |
| 57. Dic173 | #108 | semidirect |
| 63. C173 | C4×#108 | semidirect |
| 120. C4 | #19149750 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149750 | 2 |
| C4×#14583836 | 2 |
| #26012367 | 2 |
| C4×C8×D173 | 2 |
| C4×#108 | 173 |