Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
552 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 213 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. C22×#15668432 | C2 | semidirect |
| 3. #26041356 | C2 | direct (N × H) |
| 4. C2×#19153728 | C2 | semidirect |
| 5. C2×C4×#13089678 | C2 | semidirect |
| 6. C2×C4⋊C8×C181 | C2 | semidirect |
| 10. C2×#15668432 | C22 | semidirect |
| 17. #19153728 | C22 | semidirect |
| 18. C4×#13089678 | C22 | semidirect |
| 21. C4⋊C8×C181 | C22 | semidirect |
| 32. C2×#13089678 | D4 | semidirect |
| 55. #13089678 | C2×D4 | semidirect |
| 58. C2×C4×C181 | M16 | semidirect |
| 76. C4×C181 | C2×M16 | semidirect |
| 80. C2×C181 | #436 | semidirect |
| 85. C181 | C2×#436 | semidirect |
| 90. C2×C4⋊C8 | D181 | semidirect |
| 105. C4⋊C8 | C2×D181 | semidirect |
| 142. C2×C4 | #15668432 | semidirect |
| 163. C4 | C2×#15668432 | semidirect |
| 167. C2 | #26041356 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668432 | 2 |
| C2×C4×D724 | 2 |
| #26041356 | 2 |
| C2×#19153728 | 2 |
| C2×C4×#13089678 | 2 |
| C2×C4⋊C8×C181 | 2 |
| C2×#436 | 181 |