Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
374 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#19153740 | C2 | semidirect |
| 5. #26041041 | C2 | semidirect |
| 6. #26041034 | C2 | semidirect |
| 7. C2×C4×Q8×C181 | C2 | semidirect |
| 11. C2×#15668436 | C4 | semidirect |
| 82. Q8×C181 | C22⋊C4 | semidirect |
| 94. C2×C4×C181 | SD16 | semidirect |
| 132. C181 | #1880 | semidirect |
| 135. C2×C4×Q8 | D181 | semidirect |
| 206. Q8 | #15668426 | semidirect |
| 225. C2×C4 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668436 | 2 |
| C2×#19153740 | 2 |
| C2×#19153736 | 2 |
| #26041181 | 2 |
| #26041041 | 2 |
| #26041034 | 2 |
| C2×C4×Q8×C181 | 2 |
| #1880 | 181 |