Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26041335 | C2 | semidirect |
| 3. C4×#15668432 | C2 | semidirect |
| 4. #26041008 | C2 | semidirect |
| 5. D4⋊#13089678 | C2 | semidirect |
| 6. #26041006 | C2 | semidirect |
| 7. D4⋊C8×C181 | C2 | semidirect |
| 19. C4⋊#13089678 | C22 | semidirect |
| 23. C4×#13089678 | C22 | semidirect |
| 25. C4⋊C8×C181 | C22 | semidirect |
| 26. C4×C8×C181 | C22 | semidirect |
| 65. D724 | M16 | semidirect |
| 85. D4×C181 | M16 | semidirect |
| 121. C181 | #1490 | semidirect |
| 129. D4⋊C8 | D181 | semidirect |
| 143. C4⋊C8 | C2×D181 | semidirect |
| 148. C4×C8 | C2×D181 | semidirect |
| 191. D4 | #15668432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×D181 | 2 |
| #26041335 | 2 |
| C4×#15668432 | 2 |
| #26041008 | 2 |
| D4⋊#13089678 | 2 |
| #26041006 | 2 |
| D4⋊C8×C181 | 2 |
| #1490 | 181 |