Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
264 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26041329 | C2 | semidirect |
| 3. #26041005 | C2 | semidirect |
| 5. #324×C181 | C2 | semidirect |
| 26. C2×C4×D181 | C8 | semidirect |
| 88. C181 | #1458 | semidirect |
| 93. #324 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153774 | 2 |
| #26041329 | 2 |
| #26041005 | 2 |
| #26041002 | 2 |
| #324×C181 | 2 |
| #1458 | 181 |