Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
644 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 3. #26041186 | C2 | semidirect |
| 4. #26041175 | C2 | semidirect |
| 5. #26041149 | C2 | semidirect |
| 7. C2×C4⋊Q8×C181 | C2 | semidirect |
| 32. C2×C4×D181 | Q8 | semidirect |
| 82. C2×D181 | C4⋊Q8 | semidirect |
| 85. C4×C181 | C22⋊Q8 | semidirect |
| 95. C181 | #2857 | semidirect |
| 97. C2×C4⋊Q8 | D181 | semidirect |
| 184. C4 | #19153792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153792 | 2 |
| C2×C42×D181 | 2 |
| #26041186 | 2 |
| #26041175 | 2 |
| #26041149 | 2 |
| #26041136 | 2 |
| C2×C4⋊Q8×C181 | 2 |
| #2857 | 181 |