Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19153727 | C2 | semidirect |
| 4. #26041033 | C2 | semidirect |
| 5. C2×C4×C8×C181 | C2 | semidirect |
| 13. #19153728 | C4 | semidirect |
| 77. C181 | #1750 | semidirect |
| 82. C2×C4×C8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153773 | 2 |
| C2×#19153728 | 2 |
| C2×#19153727 | 2 |
| #26041033 | 2 |
| C2×C4×C8×C181 | 2 |
| #1750 | 181 |