Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19153841 | C2 | semidirect |
| 2. C2×#19153813 | C2 | semidirect |
| 3. #26041479 | C2 | semidirect |
| 4. #26041474 | C2 | semidirect |
| 5. #26041303 | C2 | semidirect |
| 6. #26041283 | C2 | semidirect |
| 7. C4×#41×C181 | C2 | semidirect |
| 11. C2×#15668436 | C22 | semidirect |
| 12. C2×#15668434 | C22 | semidirect |
| 17. C4⋊#13089678 | C22 | semidirect |
| 18. #19153736 | C22 | semidirect |
| 20. C4×Q8×C181 | C22 | semidirect |
| 22. C4×D4×C181 | C22 | semidirect |
| 40. #41×C181 | D4 | semidirect |
| 69. Q8×C181 | C2×D4 | semidirect |
| 72. D4×C181 | C2×D4 | semidirect |
| 96. C4×C181 | AGL(1,ℤ/8) | semidirect |
| 104. C181 | #3038 | semidirect |
| 108. C4×#41 | D181 | semidirect |
| 123. C4×Q8 | C2×D181 | semidirect |
| 125. C4×D4 | C2×D181 | semidirect |
| 134. #41 | D724 | semidirect |
| 168. Q8 | C2×D724 | semidirect |
| 176. D4 | C2×D724 | semidirect |
| 201. C4 | #19153841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153841 | 2 |
| C2×#19153813 | 2 |
| #26041479 | 2 |
| #26041474 | 2 |
| #26041303 | 2 |
| #26041283 | 2 |
| C4×#41×C181 | 2 |
| #3038 | 181 |