Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 84 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. #22626283 | C2 | semidirect |
| 4. #22626037 | C2 | semidirect |
| 5. #22625004 | C2 | semidirect |
| 6. #22624977 | C2 | semidirect |
| 27. #17988398 | C4 | semidirect |
| 28. #17988397 | C4 | semidirect |
| 29. #17988396 | C4 | semidirect |
| 30. #360×C73 | C4 | semidirect |
| 70. #14556531 | C2×C4 | semidirect |
| 73. #14556523 | C2×C4 | semidirect |
| 76. M32×C73 | C2×C4 | semidirect |
| 77. #106×C73 | C2×C4 | semidirect |
| 113. Dic292 | C4⋊C4 | semidirect |
| 118. D584 | C4⋊C4 | semidirect |
| 129. Q16×C73 | C4⋊C4 | semidirect |
| 131. D8×C73 | C4⋊C4 | semidirect |
| 215. C73 | #12943 | semidirect |
| 235. #360 | #64408 | semidirect |
| 268. M32 | C2×#64408 | semidirect |
| 278. #106 | C2×#64408 | semidirect |
| 305. Q16 | C4⋊#64408 | semidirect |
| 312. D8 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626685 | 2 |
| #22626283 | 2 |
| #22626239 | 2 |
| #22626037 | 2 |
| #22625004 | 2 |
| #22624977 | 2 |
| #360×D73 | 2 |
| #12943 | 73 |