Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22627075 | C2 | semidirect |
| 3. #22627056 | C2 | semidirect |
| 5. #22626943 | C2 | semidirect |
| 6. #22626936 | C2 | semidirect |
| 68. #14556519 | C8 | semidirect |
| 69. #14556518 | C8 | semidirect |
| 70. #14556517 | C8 | semidirect |
| 71. #104×C73 | C8 | semidirect |
| 118. #11924012 | C2×C8 | semidirect |
| 122. C4×Dic73 | C2×C8 | semidirect |
| 124. M16×C73 | C2×C8 | semidirect |
| 125. C42×C73 | C2×C8 | semidirect |
| 148. Q8×C73 | C4⋊C8 | semidirect |
| 150. D4×C73 | C4⋊C8 | semidirect |
| 161. D292 | C4⋊C8 | semidirect |
| 172. Dic146 | C4⋊C8 | semidirect |
| 216. C73 | #8839 | semidirect |
| 272. #104 | #10596842 | semidirect |
| 302. M16 | C2×#10596842 | semidirect |
| 334. C42 | C2×#10596842 | semidirect |
| 339. Q8 | C4⋊#10596842 | semidirect |
| 346. D4 | C4⋊#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627175 | 2 |
| #22627075 | 2 |
| #22627056 | 2 |
| #22627050 | 2 |
| #22626943 | 2 |
| #22626936 | 2 |
| #104×#64408 | 2 |
| #8839 | 73 |