Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
456 conjugacy classes of subgroups; only the 305 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 305 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. Q8×#13089678 | C2 | semidirect |
| 2. D4×#13089678 | C2 | semidirect |
| 3. #26041332 | C2 | semidirect |
| 4. C2×C4×#13089678 | C2 | semidirect |
| 22. #41×C181 | C8 | semidirect |
| 36. #13089678 | #41 | direct (N × H) |
| 38. Q8×C181 | C2×C8 | semidirect |
| 39. D4×C181 | C2×C8 | semidirect |
| 42. C2×C4×C181 | C2×C8 | semidirect |
| 63. C181 | C8×#41 | semidirect |
| 83. #41 | #13089678 | direct (N × H) |
| 100. Q8 | C2×#13089678 | semidirect |
| 101. D4 | C2×#13089678 | semidirect |
| 104. C2×C4 | C2×#13089678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#13089678 | 2 |
| D4×#13089678 | 2 |
| #26041332 | 2 |
| C2×C4×#13089678 | 2 |
| C4×#41×C181 | 2 |
| C8×#41 | 181 |