Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22599258 | C2 | semidirect |
| 2. #22597804 | C2 | semidirect |
| 3. #22587008 | C2 | semidirect |
| 4. #22586834 | C2 | semidirect |
| 5. #22586731 | C2 | semidirect |
| 6. #22586243 | C2 | semidirect |
| 7. C71×#2541 | C2 | semidirect |
| 38. #14556128 | D4 | semidirect |
| 39. #14556125 | D4 | semidirect |
| 47. C4⋊(C71⋊C8) | D4 | semidirect |
| 48. C4⋊(C71⋊C8) | D4 | semidirect |
| 124. C2×D4×C71 | D8 | semidirect |
| 243. #2541 | D71 | semidirect |
| 248. C71 | #10238 | semidirect |
| 352. C2×D4 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599258 | 2 |
| #22597804 | 2 |
| #22587008 | 2 |
| #22586834 | 2 |
| #22586731 | 2 |
| #22586243 | 2 |
| C71×#2541 | 2 |
| #10238 | 71 |