Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
148 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 1. C2×#19153757 | C2 | semidirect |
| 2. #26041696 | C2 | semidirect |
| 3. #26041549 | C2 | semidirect |
| 4. #26041108 | C2 | semidirect |
| 5. #26041092 | C2 | semidirect |
| 6. #26041091 | C2 | semidirect |
| 7. #472×C181 | C2 | semidirect |
| 73. C181 | #2221 | semidirect |
| 78. #472 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153757 | 2 |
| #26041696 | 2 |
| #26041549 | 2 |
| #26041108 | 2 |
| #26041092 | 2 |
| #26041091 | 2 |
| #472×C181 | 2 |
| #2221 | 181 |