Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. #26041330 | C2 | semidirect |
| 3. #26041301 | C2 | semidirect |
| 4. #26041011 | C2 | semidirect |
| 5. #26041009 | C2 | semidirect |
| 6. D4⋊#13089678 | C2 | semidirect |
| 7. D4⋊C8×C181 | C2 | semidirect |
| 105. C181 | #1495 | semidirect |
| 113. D4⋊C8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041811 | 2 |
| #26041330 | 2 |
| #26041301 | 2 |
| #26041011 | 2 |
| #26041009 | 2 |
| D4⋊#13089678 | 2 |
| D4⋊C8×C181 | 2 |
| #1495 | 181 |