Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 1. #26042045 | C2 | semidirect |
| 3. #26041261 | C2 | semidirect |
| 4. C2×#19153733 | C2 | semidirect |
| 5. #26041051 | C2 | semidirect |
| 6. #26041050 | C2 | semidirect |
| 7. C2×#100×C181 | C2 | semidirect |
| 38. #15668433 | D4 | semidirect |
| 58. M16×C181 | D4 | semidirect |
| 114. C181 | #1914 | semidirect |
| 120. C2×#100 | D181 | semidirect |
| 166. M16 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042045 | 2 |
| #26041846 | 2 |
| #26041261 | 2 |
| C2×#19153733 | 2 |
| #26041051 | 2 |
| #26041050 | 2 |
| C2×#100×C181 | 2 |
| #1914 | 181 |