Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
924 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 210 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×D4×#10624382 | C2 | semidirect |
| 2. #26042231 | C2 | semidirect |
| 3. #26042225 | C2 | semidirect |
| 4. C42×#10624382 | C2 | semidirect |
| 13. #19153813 | C4 | semidirect |
| 14. #19153812 | C4 | semidirect |
| 16. #127×C181 | C4 | semidirect |
| 24. C4×#10624382 | D4 | semidirect |
| 26. C2×D724 | C2×C4 | semidirect |
| 27. C2×C22⋊D181 | C2×C4 | semidirect |
| 31. C4×Dic181 | C2×C4 | semidirect |
| 32. C2×D4×C181 | C2×C4 | semidirect |
| 33. C42×C181 | C2×C4 | semidirect |
| 60. #10624382 | #127 | direct (N × H) |
| 61. C4×C181 | C4×D4 | semidirect |
| 62. Dic181 | C4×D4 | semidirect |
| 68. C181 | C4×#127 | semidirect |
| 79. #127 | #10624382 | direct (N × H) |
| 91. C2×D4 | C2×#10624382 | semidirect |
| 102. C42 | C2×#10624382 | semidirect |
| 131. C4 | D4×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#10624382 | 2 |
| #26042231 | 2 |
| #26042225 | 2 |
| C42×#10624382 | 2 |
| #127×D181 | 2 |
| C4×#127 | 181 |