Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19153838 | C2 | semidirect |
| 2. #26041711 | C2 | direct (N × H) |
| 3. C2×Dic1448 | C2 | semidirect |
| 4. C2×#19153761 | C2 | semidirect |
| 5. C2×D2896 | C2 | semidirect |
| 6. C22×C16×C181 | C2 | semidirect |
| 9. #19153838 | C22 | semidirect |
| 13. Dic1448 | C22 | semidirect |
| 14. #19153761 | C22 | semidirect |
| 15. D2896 | C22 | semidirect |
| 19. C2×C16×C181 | C22 | semidirect |
| 64. C2×C181 | #508 | semidirect |
| 67. C181 | C2×#508 | semidirect |
| 74. C22×C16 | D181 | semidirect |
| 87. C2×C16 | C2×D181 | semidirect |
| 133. C2 | #26041711 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153838 | 2 |
| #26041711 | 2 |
| C2×Dic1448 | 2 |
| C2×#19153761 | 2 |
| C2×D2896 | 2 |
| C22×C16×C181 | 2 |
| C2×#508 | 181 |