Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#19153741 | C2 | semidirect |
| 3. C2×#19153739 | C2 | semidirect |
| 4. C2×#19153737 | C2 | semidirect |
| 5. C2×#19153728 | C2 | semidirect |
| 6. #26041136 | C2 | semidirect |
| 7. C2×#102×C181 | C2 | semidirect |
| 13. C2×#15668448 | C4 | semidirect |
| 86. Dic362 | C22⋊C4 | semidirect |
| 114. D4×C181 | C22⋊C4 | semidirect |
| 163. C181 | #1788 | semidirect |
| 169. C2×#102 | D181 | semidirect |
| 263. D4 | #15668426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668448 | 2 |
| C2×#19153741 | 2 |
| C2×#19153739 | 2 |
| C2×#19153737 | 2 |
| C2×#19153728 | 2 |
| #26041136 | 2 |
| C2×#102×C181 | 2 |
| #1788 | 181 |