Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 162 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. #26042230 | C2 | semidirect |
| 3. #26042229 | C2 | semidirect |
| 4. #26042222 | C2 | semidirect |
| 5. #26042221 | C2 | semidirect |
| 6. C4×C4⋊#10624382 | C2 | semidirect |
| 7. #26042215 | C2 | semidirect |
| 22. C4×D724 | C4 | semidirect |
| 23. D4×Dic181 | C4 | semidirect |
| 24. #19153778 | C4 | semidirect |
| 25. C4×C22⋊D181 | C4 | semidirect |
| 26. #19153776 | C4 | semidirect |
| 30. C4×D4×C181 | C4 | semidirect |
| 132. C181 | #2319 | semidirect |
| 149. C4×D4 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042231 | 2 |
| #26042230 | 2 |
| #26042229 | 2 |
| #26042222 | 2 |
| #26042221 | 2 |
| C4×C4⋊#10624382 | 2 |
| #26042215 | 2 |
| C4×D4×D181 | 2 |
| #2319 | 181 |