Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
122 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 25 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. #26011284 | C2 | semidirect |
| 2. #26011235 | C2 | semidirect |
| 6. H(5,𝔽2)×C173 | C4 | semidirect |
| 10. #100×C173 | C4 | semidirect |
| 59. C173 | #1402 | semidirect |
| 64. H(5,𝔽2) | Dic173 | semidirect |
| 69. #100 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011284 | 2 |
| #26011235 | 2 |
| #453×C173 | 2 |
| #1402 | 173 |