Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
224 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 4. #26011213 | C2 | semidirect |
| 5. #26011212 | C2 | semidirect |
| 6. C8×#13063436 | C2 | semidirect |
| 7. C82×C173 | C2 | semidirect |
| 24. #14583809 | C8 | direct (N × H) |
| 45. #13063436 | C2×C8 | semidirect |
| 50. C8×C173 | C2×C8 | semidirect |
| 51. C8×C173 | M16 | semidirect |
| 66. C173 | C8×M16 | semidirect |
| 74. C82 | D173 | semidirect |
| 117. C8 | C8×D173 | semidirect |
| 118. C8 | #14583809 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011542 | 2 |
| C4×#14583809 | 2 |
| C4×C8×D173 | 2 |
| #26011213 | 2 |
| #26011212 | 2 |
| C8×#13063436 | 2 |
| C82×C173 | 2 |
| C8×M16 | 173 |