Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
234 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26041231 | C2 | semidirect |
| 3. #97×D181 | C2 | semidirect |
| 4. #26041021 | C2 | semidirect |
| 5. #26041018 | C2 | semidirect |
| 6. #26041018 | C2 | semidirect |
| 7. #330×C181 | C2 | semidirect |
| 99. C181 | #1524 | semidirect |
| 105. #330 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041814 | 2 |
| #26041231 | 2 |
| #97×D181 | 2 |
| #26041021 | 2 |
| #26041018 | 2 |
| #330×C181 | 2 |
| #1524 | 181 |