Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
432 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 297 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 |
| 38. Q8×C181 | C2×C8 | semidirect |
| 39. D4×C181 | C2×C8 | semidirect |
| 43. C2×C4×C181 | C2×C8 | semidirect |
| 65. C181 | #2988 | semidirect |
| 85. #41 | #13089678 | semidirect |
| 102. Q8 | C2×#13089678 | semidirect |
| 103. D4 | C2×#13089678 | semidirect |
| 107. 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 |
| #2988 | 181 |