Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15668439 | C2 | semidirect |
| 3. #26041658 | C2 | semidirect |
| 4. #26041518 | C2 | semidirect |
| 5. #26041489 | C2 | semidirect |
| 6. #26041486 | C2 | semidirect |
| 7. #26041435 | C2 | semidirect |
| 8. #26041434 | C2 | semidirect |
| 9. C4×#15668439 | C2 | semidirect |
| 52. #15668439 | D4 | direct (N × H) |
| 100. D4×C181 | Q16 | semidirect |
| 113. C22×C181 | C2×Q16 | semidirect |
| 120. C4×C181 | C2×Q16 | semidirect |
| 130. C181 | D4×Q16 | semidirect |
| 224. D4 | #15668439 | direct (N × H) |
| 244. C22 | C2×#15668439 | semidirect |
| 254. C4 | C2×#15668439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668439 | 2 |
| D4×Dic362 | 2 |
| #26041658 | 2 |
| #26041518 | 2 |
| #26041489 | 2 |
| #26041486 | 2 |
| #26041435 | 2 |
| #26041434 | 2 |
| C4×#15668439 | 2 |
| D4×#13089678 | 2 |
| D4×Q8×C181 | 2 |
| D4×Q16 | 181 |