Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
612 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 170 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×Q8×#10624382 | C2 | semidirect |
| 3. (C2×#10624382)⋊Q8 | C2 | semidirect |
| 5. #26042229 | C2 | semidirect |
| 6. #26042226 | C2 | semidirect |
| 7. #26042225 | C2 | semidirect |
| 8. #26042215 | C2 | semidirect |
| 27. #19153805 | C4 | semidirect |
| 28. #19153804 | C4 | semidirect |
| 29. #19153803 | C4 | semidirect |
| 30. #19153802 | C4 | semidirect |
| 33. #124×C181 | C4 | semidirect |
| 51. C2×Dic362 | C2×C4 | semidirect |
| 52. C2×Dic362 | C2×C4 | semidirect |
| 62. C22⋊Dic181 | C2×C4 | semidirect |
| 63. #15668426 | C2×C4 | semidirect |
| 64. #15668426 | C2×C4 | semidirect |
| 65. C4×Dic181 | C2×C4 | semidirect |
| 66. C4×Dic181 | C2×C4 | semidirect |
| 67. C2×Q8×C181 | C2×C4 | semidirect |
| 69. C22⋊C4×C181 | C2×C4 | semidirect |
| 70. C42×C181 | C2×C4 | semidirect |
| 138. C181 | #2326 | semidirect |
| 156. #124 | #10624382 | semidirect |
| 178. C2×Q8 | C2×#10624382 | semidirect |
| 203. C22⋊C4 | C2×#10624382 | semidirect |
| 209. C42 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10624382 | 2 |
| C2×D4×#10624382 | 2 |
| (C2×#10624382)⋊Q8 | 2 |
| #26042231 | 2 |
| #26042229 | 2 |
| #26042226 | 2 |
| #26042225 | 2 |
| #26042215 | 2 |
| #124×D181 | 2 |
| #2326 | 181 |