Finite Group DatabasebetaFinite Group DatabasebetaOrder 24704.
368 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 68 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×C193 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C193 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C193 ◁ C22×C4×C193 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #534×C193 | C2 | semidirect |
| 2. #447×C193 | C2 | semidirect |
| 3. #392×C193 | C2 | semidirect |
| 4. #327×C193 | C2 | semidirect |
| 5. #323×C193 | C2 | semidirect |
| 8. C22×D4×C193 | C22 | semidirect |
| 17. C22⋊C8×C193 | C22 | semidirect |
| 18. #95×C193 | C22 | semidirect |
| 32. C2×D4×C193 | D4 | semidirect |
| 40. C4⋊C4×C193 | D4 | semidirect |
| 60. C23×C193 | D8 | semidirect |
| 113. C193 | #1595 | direct (N × H) |
| 114. #1595 | C193 | direct (N × H) |
| 115. #534 | C2×C193 | semidirect |
| 116. #447 | C2×C193 | semidirect |
| 117. #392 | C2×C193 | semidirect |
| 118. #327 | C2×C193 | semidirect |
| 119. #323 | C2×C193 | semidirect |
| 122. C22×D4 | C22×C193 | semidirect |
| 131. C22⋊C8 | C22×C193 | semidirect |
| 132. #95 | C22×C193 | semidirect |
| 146. C2×D4 | D4×C193 | semidirect |
| 154. C4⋊C4 | D4×C193 | semidirect |
| 174. C23 | D8×C193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #534×C193 | 2 |
| #447×C193 | 2 |
| #392×C193 | 2 |
| #327×C193 | 2 |
| #323×C193 | 2 |
| #1595 | 193 |