Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
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. #22620851 | C2 | semidirect |
| 2. #22619397 | C2 | semidirect |
| 3. #22614873 | C2 | semidirect |
| 4. #22608600 | C2 | semidirect |
| 5. #22608425 | C2 | semidirect |
| 6. #22608321 | C2 | semidirect |
| 7. C73×#1303 | C2 | semidirect |
| 43. #14556591 | D4 | semidirect |
| 50. #14556588 | D4 | semidirect |
| 75. C4⋊C8×C73 | D4 | semidirect |
| 76. C4⋊C8×C73 | D4 | semidirect |
| 110. C2×D292 | D8 | semidirect |
| 247. #1303 | D73 | semidirect |
| 248. C73 | #10238 | semidirect |
| 311. C4⋊C8 | D292 | semidirect |
| 312. C4⋊C8 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620851 | 2 |
| #22619397 | 2 |
| #22614873 | 2 |
| #22608600 | 2 |
| #22608425 | 2 |
| #22608321 | 2 |
| C73×#1303 | 2 |
| #10238 | 73 |