Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1184 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C73 |
| socle | C2×C73 | C2×B(4,𝔽2) |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C2×C4×C73 ◁ C2×#41×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C73×#3483 | C2 | semidirect |
| 2. C73×#3018 | C2 | semidirect |
| 3. C73×#2205 | C2 | semidirect |
| 4. C73×#2204 | C2 | semidirect |
| 5. C73×#2132 | C2 | semidirect |
| 8. Q82×C73 | C22 | semidirect |
| 10. #555×C73 | C22 | semidirect |
| 21. #356×C73 | C22 | semidirect |
| 22. #355×C73 | C22 | semidirect |
| 163. #33567 | C73 | direct (N × H) |
| 169. #3483 | C2×C73 | semidirect |
| 170. #3018 | C2×C73 | semidirect |
| 171. #2205 | C2×C73 | semidirect |
| 172. #2204 | C2×C73 | semidirect |
| 173. #2132 | C2×C73 | semidirect |
| 174. C73 | #33567 | direct (N × H) |
| 177. Q82 | C22×C73 | semidirect |
| 179. #555 | C22×C73 | semidirect |
| 190. #356 | C22×C73 | semidirect |
| 191. #355 | C22×C73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#3483 | 2 |
| C73×#3018 | 2 |
| C73×#2205 | 2 |
| C73×#2204 | 2 |
| C73×#2132 | 2 |
| #33567 | 73 |