Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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. #101×D181 | C2 | semidirect |
| 3. #26041076 | C2 | semidirect |
| 4. #26041075 | C2 | semidirect |
| 5. #355×C181 | C2 | semidirect |
| 15. #19153735 | C22 | semidirect |
| 18. #101×C181 | C22 | semidirect |
| 90. D181 | #355 | direct (N × H) |
| 91. C181 | C2×#355 | semidirect |
| 97. #355 | D181 | direct (N × H) |
| 110. #101 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #124×D181 | 2 |
| #101×D181 | 2 |
| #26041076 | 2 |
| #26041075 | 2 |
| #355×C181 | 2 |
| C2×#355 | 181 |