Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
474 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#15668436 | C2 | semidirect |
| 3. C2×#19153738 | C2 | semidirect |
| 4. C2×#19153737 | C2 | semidirect |
| 5. #26041186 | C2 | semidirect |
| 6. #26041033 | C2 | semidirect |
| 7. C22×SD16×C181 | C2 | semidirect |
| 42. C2×#13089678 | D4 | semidirect |
| 53. C2×Q8×C181 | D4 | semidirect |
| 65. C2×C8×C181 | D4 | semidirect |
| 80. C2×Dic181 | SD16 | semidirect |
| 135. C181 | #2014 | semidirect |
| 138. C22×SD16 | D181 | semidirect |
| 170. C2×Q8 | C22⋊D181 | semidirect |
| 197. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668436 | 2 |
| C2×#19153812 | 2 |
| C2×#19153738 | 2 |
| C2×#19153737 | 2 |
| #26041186 | 2 |
| #26041033 | 2 |
| C22×SD16×C181 | 2 |
| #2014 | 181 |