Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
642 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C107 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C107 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C107×#3253 | C2 | semidirect |
| 2. C107×#3205 | C2 | semidirect |
| 3. C107×#3151 | C2 | semidirect |
| 4. C107×#1965 | C2 | semidirect |
| 5. C107×#1525 | C2 | semidirect |
| 6. C107×#1484 | C2 | semidirect |
| 7. C107×#1299 | C2 | semidirect |
| 196. #10104 | C107 | direct (N × H) |
| 204. #3253 | C2×C107 | semidirect |
| 205. #3205 | C2×C107 | semidirect |
| 206. #3151 | C2×C107 | semidirect |
| 207. #1965 | C2×C107 | semidirect |
| 208. #1525 | C2×C107 | semidirect |
| 209. #1484 | C2×C107 | semidirect |
| 210. #1299 | C2×C107 | semidirect |
| 211. C107 | #10104 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#3253 | 2 |
| C107×#3205 | 2 |
| C107×#3151 | 2 |
| C107×#1965 | 2 |
| C107×#1525 | 2 |
| C107×#1484 | 2 |
| C107×#1299 | 2 |
| #10104 | 107 |