Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22597800 | C2 | semidirect |
| 2. #22593287 | C2 | semidirect |
| 3. #22587008 | C2 | semidirect |
| 4. #22586835 | C2 | semidirect |
| 5. #22586730 | C2 | semidirect |
| 6. #22586242 | C2 | semidirect |
| 7. C71×#3205 | C2 | semidirect |
| 53. C4⋊(C71⋊C8) | D4 | semidirect |
| 64. C4⋊Q8×C71 | D4 | semidirect |
| 69. #127×C71 | D4 | semidirect |
| 76. C4⋊C8×C71 | D4 | semidirect |
| 86. C2×D284 | D8 | semidirect |
| 241. #3205 | D71 | semidirect |
| 248. C71 | #10238 | semidirect |
| 285. C4⋊Q8 | C22⋊D71 | semidirect |
| 292. #127 | C22⋊D71 | semidirect |
| 312. C4⋊C8 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597800 | 2 |
| #22593287 | 2 |
| #22587008 | 2 |
| #22586835 | 2 |
| #22586730 | 2 |
| #22586242 | 2 |
| C71×#3205 | 2 |
| #10238 | 71 |