Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1160 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C73 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C23×C4×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#447×C73 | C2 | semidirect |
| 2. C73×#2656 | C2 | semidirect |
| 3. C2×#327×C73 | C2 | semidirect |
| 4. C73×#1438 | C2 | semidirect |
| 5. C73×#1280 | C2 | semidirect |
| 28. C22×D4×C73 | D4 | semidirect |
| 50. C22⋊C8×C73 | D4 | semidirect |
| 92. C22×C4×C73 | D8 | semidirect |
| 204. #9962 | C73 | direct (N × H) |
| 215. C2×#447 | C2×C73 | semidirect |
| 216. #2656 | C2×C73 | semidirect |
| 217. C2×#327 | C2×C73 | semidirect |
| 218. #1438 | C2×C73 | semidirect |
| 219. #1280 | C2×C73 | semidirect |
| 220. C73 | #9962 | direct (N × H) |
| 243. C22×D4 | D4×C73 | semidirect |
| 265. C22⋊C8 | D4×C73 | semidirect |
| 307. C22×C4 | D8×C73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#447×C73 | 2 |
| C73×#2656 | 2 |
| C2×#327×C73 | 2 |
| C73×#1438 | 2 |
| C73×#1280 | 2 |
| #9962 | 73 |