Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
394 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 179 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. Q8×#13089678 | C2 | semidirect |
| 3. #26041358 | C2 | semidirect |
| 4. #26041356 | C2 | semidirect |
| 5. #26041330 | C2 | semidirect |
| 6. #26041301 | C2 | semidirect |
| 7. C8×Q8×C181 | C2 | semidirect |
| 53. Q8×C181 | M16 | semidirect |
| 74. C181 | #2991 | semidirect |
| 78. C8×Q8 | D181 | semidirect |
| 118. Q8 | #15668432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668450 | 2 |
| Q8×#13089678 | 2 |
| #26041358 | 2 |
| #26041356 | 2 |
| #26041330 | 2 |
| #26041301 | 2 |
| C8×Q8×C181 | 2 |
| #2991 | 181 |