Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
378 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C107 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C107 ◁ C42×C107 ◁ C8×Q8×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C107×#3391 | C2 | semidirect |
| 2. C107×#2246 | C2 | semidirect |
| 3. C107×#2206 | C2 | semidirect |
| 4. C107×#1668 | C2 | semidirect |
| 5. C107×#1361 | C2 | semidirect |
| 6. C107×Q8⋊C16 | C2 | semidirect |
| 7. C107×#1331 | C2 | semidirect |
| 95. Q8×C107 | D16 | semidirect |
| 142. #12328 | C107 | direct (N × H) |
| 149. #3391 | C2×C107 | semidirect |
| 150. #2246 | C2×C107 | semidirect |
| 151. #2206 | C2×C107 | semidirect |
| 152. #1668 | C2×C107 | semidirect |
| 153. #1361 | C2×C107 | semidirect |
| 154. Q8⋊C16 | C2×C107 | semidirect |
| 155. #1331 | C2×C107 | semidirect |
| 156. C107 | #12328 | direct (N × H) |
| 244. Q8 | D16×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#3391 | 2 |
| C107×#2246 | 2 |
| C107×#2206 | 2 |
| C107×#1668 | 2 |
| C107×#1361 | 2 |
| C107×Q8⋊C16 | 2 |
| C107×#1331 | 2 |
| #12328 | 107 |