Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
610 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22589180 | C2 | semidirect |
| 3. #22587099 | C2 | semidirect |
| 4. #22587007 | C2 | semidirect |
| 5. C8×M16×C71 | C2 | semidirect |
| 64. M16×C71 | D8 | semidirect |
| 99. C8×C71 | #100 | semidirect |
| 126. C8×M16 | D71 | semidirect |
| 127. C71 | #9802 | semidirect |
| 185. M16 | D568 | semidirect |
| 222. C8 | #14556044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986376 | 2 |
| #22589180 | 2 |
| #22587099 | 2 |
| #22587007 | 2 |
| C8×M16×C71 | 2 |
| #9802 | 71 |