Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
368 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 90 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×C103 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C103 |
| prime radical | C2×D4×C103 | D8 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C42×C103 ◁ C8×D4×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C103×#2247 | C2 | semidirect |
| 3. C103×#2209 | C2 | semidirect |
| 5. C103×#1362 | C2 | semidirect |
| 6. C103×#1332 | C2 | semidirect |
| 103. D4×C103 | Q32 | semidirect |
| 134. #12322 | C103 | direct (N × H) |
| 140. #2247 | C2×C103 | semidirect |
| 141. #2209 | C2×C103 | semidirect |
| 143. #1362 | C2×C103 | semidirect |
| 144. #1332 | C2×C103 | semidirect |
| 146. C103 | #12322 | direct (N × H) |
| 242. D4 | Q32×C103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q16×C103 | 2 |
| C103×#2247 | 2 |
| C103×#2209 | 2 |
| C103×#1669 | 2 |
| C103×#1362 | 2 |
| C103×#1332 | 2 |
| C103×D4⋊C16 | 2 |
| #12322 | 103 |