Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #26041629 | C2 | semidirect |
| 3. #26041607 | C2 | semidirect |
| 4. #26041564 | C2 | semidirect |
| 5. #26041510 | C2 | semidirect |
| 6. #26041481 | C2 | semidirect |
| 7. #26041418 | C2 | semidirect |
| 8. C4×#15668436 | C2 | semidirect |
| 9. D4×#13089678 | C2 | semidirect |
| 10. C2×#19153740 | C2 | semidirect |
| 11. D4×Q8×C181 | C2 | semidirect |
| 94. Q8×C181 | #41 | semidirect |
| 95. D4×C181 | SD16 | semidirect |
| 128. C181 | #3298 | semidirect |
| 130. D4×Q8 | D181 | semidirect |
| 213. Q8 | #15668448 | semidirect |
| 217. D4 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041933 | 2 |
| #26041629 | 2 |
| #26041607 | 2 |
| #26041564 | 2 |
| #26041510 | 2 |
| #26041481 | 2 |
| #26041418 | 2 |
| C4×#15668436 | 2 |
| D4×#13089678 | 2 |
| C2×#19153740 | 2 |
| D4×Q8×C181 | 2 |
| #3298 | 181 |