Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. C2×#19153726 | C2 | semidirect |
| 5. #26041034 | C2 | semidirect |
| 6. #26041033 | C2 | semidirect |
| 7. C2×C4×C8×C181 | C2 | semidirect |
| 11. C2×#15668432 | C4 | semidirect |
| 16. #19153728 | C4 | semidirect |
| 72. C2×C4×C181 | M16 | semidirect |
| 80. C8×C181 | C22⋊C4 | semidirect |
| 104. C181 | #1753 | semidirect |
| 109. C2×C4×C8 | D181 | semidirect |
| 175. C2×C4 | #15668432 | semidirect |
| 185. C8 | #15668426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668432 | 2 |
| C2×#19153728 | 2 |
| C2×#19153726 | 2 |
| C4×#15668426 | 2 |
| #26041034 | 2 |
| #26041033 | 2 |
| C2×C4×C8×C181 | 2 |
| #1753 | 181 |