Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31826769 | C2 | semidirect |
| 3. #31826762 | C2 | semidirect |
| 4. #31826505 | C2 | semidirect |
| 5. #31826489 | C2 | semidirect |
| 7. C2×#125×C283 | C2 | semidirect |
| 90. C283 | #3080 | semidirect |
| 92. C2×#125 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#17985392 | 2 |
| #31826769 | 2 |
| #31826762 | 2 |
| #31826505 | 2 |
| #31826489 | 2 |
| #31826464 | 2 |
| C2×#125×C283 | 2 |
| #3080 | 283 |