Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. #26041574 | C2 | semidirect |
| 4. #26041489 | C2 | semidirect |
| 6. C4×#15668439 | C2 | semidirect |
| 78. C2×C4×C181 | Q16 | semidirect |
| 103. C181 | #3104 | semidirect |
| 181. C2×C4 | #15668439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041836 | 2 |
| #26041614 | 2 |
| #26041574 | 2 |
| #26041489 | 2 |
| #26041435 | 2 |
| C4×#15668439 | 2 |
| #26041332 | 2 |
| C2×C4×Q8×C181 | 2 |
| #3104 | 181 |