Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
370 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 370 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. Q8×Dic362 | C2 | semidirect |
| 3. #26041677 | C2 | semidirect |
| 5. #26041565 | C2 | semidirect |
| 7. C8×Q8×C181 | C2 | semidirect |
| 30. #15668438 | Q8 | direct (N × H) |
| 47. Dic362 | C2×Q8 | semidirect |
| 54. Q8×C181 | SD16 | semidirect |
| 59. C8×C181 | C2×Q8 | semidirect |
| 75. C181 | Q8×SD16 | semidirect |
| 82. C8×Q8 | D181 | semidirect |
| 124. Q8 | #15668438 | direct (N × H) |
| 135. C8 | Q8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic362 | 2 |
| Q8×D724 | 2 |
| #26041677 | 2 |
| #26041570 | 2 |
| #26041565 | 2 |
| C4×#15668438 | 2 |
| C8×Q8×C181 | 2 |
| Q8×SD16 | 181 |