Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#19153730 | C2 | semidirect |
| 3. #26041159 | C2 | semidirect |
| 4. #26041156 | C2 | semidirect |
| 5. #26041154 | C2 | semidirect |
| 6. #26041045 | C2 | semidirect |
| 7. C2×#99×C181 | C2 | semidirect |
| 73. C22⋊C4×C181 | D4 | semidirect |
| 175. C181 | #2044 | semidirect |
| 179. C2×#99 | D181 | semidirect |
| 249. C22⋊C4 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041838 | 2 |
| C2×#19153730 | 2 |
| #26041159 | 2 |
| #26041156 | 2 |
| #26041154 | 2 |
| #26041045 | 2 |
| C2×#99×C181 | 2 |
| #2044 | 181 |