Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. C22×D1136 | C2 | semidirect |
| 2. C2×#17986415 | C2 | semidirect |
| 3. #22597989 | C2 | semidirect |
| 4. #22590444 | C2 | semidirect |
| 5. #22590427 | C2 | semidirect |
| 6. #22590055 | C2 | semidirect |
| 7. C71×#2158 | C2 | semidirect |
| 16. C2×#14556067 | C22 | semidirect |
| 17. C2×C16×D71 | C22 | semidirect |
| 19. #17986236 | C22 | semidirect |
| 21. #17985799 | C22 | semidirect |
| 24. #367×C71 | C22 | semidirect |
| 25. #366×C71 | C22 | semidirect |
| 50. C2×C16×C71 | D4 | semidirect |
| 135. #2158 | D71 | semidirect |
| 137. C71 | #33607 | semidirect |
| 153. #367 | C2×D71 | semidirect |
| 154. #366 | C2×D71 | semidirect |
| 179. C2×C16 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1136 | 2 |
| C2×#17986415 | 2 |
| #22597989 | 2 |
| #22590444 | 2 |
| #22590427 | 2 |
| #22590055 | 2 |
| C71×#2158 | 2 |
| #33607 | 71 |